Why is A union B also called “A or B”?





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$begingroup$


In A union B, the element either belongs to A or B, or A and B right?
So shouldn't it be called A and/or B? Due to this I am unable to solve a problem in my textbook.






elementary-set-theory







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$endgroup$











  • 5




    $begingroup$
    In math, "or" is inclusive.
    $endgroup$
    – quasi
    May 28 at 12:33










  • $begingroup$
    Where is A union B also called "A or B"?
    $endgroup$
    – Hagen von Eitzen
    May 28 at 12:34






  • 2




    $begingroup$
    When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
    $endgroup$
    – Manuel DaGeo
    May 28 at 12:34










  • $begingroup$
    A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
    $endgroup$
    – Michael
    May 28 at 17:00










  • $begingroup$
    @quasi I honestly think that's the best answer out of all of the ones below.
    $endgroup$
    – Bladewood
    May 28 at 20:38


















1














$begingroup$


In A union B, the element either belongs to A or B, or A and B right?
So shouldn't it be called A and/or B? Due to this I am unable to solve a problem in my textbook.






elementary-set-theory







share|cite|improve this question










$endgroup$











  • 5




    $begingroup$
    In math, "or" is inclusive.
    $endgroup$
    – quasi
    May 28 at 12:33










  • $begingroup$
    Where is A union B also called "A or B"?
    $endgroup$
    – Hagen von Eitzen
    May 28 at 12:34






  • 2




    $begingroup$
    When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
    $endgroup$
    – Manuel DaGeo
    May 28 at 12:34










  • $begingroup$
    A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
    $endgroup$
    – Michael
    May 28 at 17:00










  • $begingroup$
    @quasi I honestly think that's the best answer out of all of the ones below.
    $endgroup$
    – Bladewood
    May 28 at 20:38














1












1








1





$begingroup$


In A union B, the element either belongs to A or B, or A and B right?
So shouldn't it be called A and/or B? Due to this I am unable to solve a problem in my textbook.






elementary-set-theory







share|cite|improve this question










$endgroup$




In A union B, the element either belongs to A or B, or A and B right?
So shouldn't it be called A and/or B? Due to this I am unable to solve a problem in my textbook.






elementary-set-theory




elementary-set-theory






share|cite|improve this question














share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked May 28 at 12:29









user662650user662650

566 bronze badges




566 bronze badges











  • 5




    $begingroup$
    In math, "or" is inclusive.
    $endgroup$
    – quasi
    May 28 at 12:33










  • $begingroup$
    Where is A union B also called "A or B"?
    $endgroup$
    – Hagen von Eitzen
    May 28 at 12:34






  • 2




    $begingroup$
    When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
    $endgroup$
    – Manuel DaGeo
    May 28 at 12:34










  • $begingroup$
    A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
    $endgroup$
    – Michael
    May 28 at 17:00










  • $begingroup$
    @quasi I honestly think that's the best answer out of all of the ones below.
    $endgroup$
    – Bladewood
    May 28 at 20:38














  • 5




    $begingroup$
    In math, "or" is inclusive.
    $endgroup$
    – quasi
    May 28 at 12:33










  • $begingroup$
    Where is A union B also called "A or B"?
    $endgroup$
    – Hagen von Eitzen
    May 28 at 12:34






  • 2




    $begingroup$
    When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
    $endgroup$
    – Manuel DaGeo
    May 28 at 12:34










  • $begingroup$
    A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
    $endgroup$
    – Michael
    May 28 at 17:00










  • $begingroup$
    @quasi I honestly think that's the best answer out of all of the ones below.
    $endgroup$
    – Bladewood
    May 28 at 20:38








5




5




$begingroup$
In math, "or" is inclusive.
$endgroup$
– quasi
May 28 at 12:33




$begingroup$
In math, "or" is inclusive.
$endgroup$
– quasi
May 28 at 12:33












$begingroup$
Where is A union B also called "A or B"?
$endgroup$
– Hagen von Eitzen
May 28 at 12:34




$begingroup$
Where is A union B also called "A or B"?
$endgroup$
– Hagen von Eitzen
May 28 at 12:34




2




2




$begingroup$
When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
$endgroup$
– Manuel DaGeo
May 28 at 12:34




$begingroup$
When we say "or" in mathematics we mean one thing, the other or both. That is why we can say the union of two sets $A cup B$ is the set whose elements are in $A$ or in $B$ (it can be in both sets).
$endgroup$
– Manuel DaGeo
May 28 at 12:34












$begingroup$
A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
$endgroup$
– Michael
May 28 at 17:00




$begingroup$
A correct answer is contained in the union of all answers given below. Does that imply that only one answer below is correct?
$endgroup$
– Michael
May 28 at 17:00












$begingroup$
@quasi I honestly think that's the best answer out of all of the ones below.
$endgroup$
– Bladewood
May 28 at 20:38




$begingroup$
@quasi I honestly think that's the best answer out of all of the ones below.
$endgroup$
– Bladewood
May 28 at 20:38










5 Answers
5






active

oldest

votes


















5
















$begingroup$

Because the elements of $A cup B$ are exactly those objects that belong to $A$ or belong to $B$.






share|cite|improve this answer










$endgroup$











  • 1




    $begingroup$
    I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
    $endgroup$
    – nuala
    May 28 at 21:12





















3
















$begingroup$

The claim "$p$ or $q$" is true if either $p$ is true, or $q$ is true, or $p$ and $q$ are both true.



That is, the claim "I am human or I am over one meter tall" is true, because at least one of the subclaims is true (in this case, both are true)






share|cite|improve this answer










$endgroup$























    3
















    $begingroup$

    Suppose we are in a university.



    The President orders ( for some reason we do not care about) the following thing: I want all math students and all students that play tennis to be present in the great hall tomorrow ( and no other person).



    The next day, due to the strong authority of the President, all math students and all students playing tennis are present in the great hall.



    Certainly, the President has in front of him all the members of the set : M U T ( that is the union of set M and of set T)



    with M = the set of all math students
    and T = the set of students playing tennis.



    Now, what does the President know of any one of the students present there ( although he has possibly never met anyone of these students before)?



    For example, what does the President know about David, one of the students that is there?



    The only thing he knows for sure is that :



    David is a math student OR David is a student that plays tennis.



    Remark : of course, it could be the case David to be both a math student and a tennis player; but of this, the President has absolutely not idea.



    In other words he only knows for sure that : one at least of these two propositions is true :



    (1) David is a math student



    (2) David is a student that plays tennis



    and this " at least one" is precisely what defines the inclusive OR operator in logic.



    Since the same thing could be said about any student, one can say in general that :



    The set : M U T is the set of all x such that (1) x is a math student OR (2) x is a student that plays tennis.



    In symbols : M U T = { x | x belongs to M v x belongs to T }



    You might say : but there are certainly students in the hall that both are maths students and play tennis.



    You would be right, but notice that if a student, say, David is both a math student and a tennis player, this is precisely an excellent reason to say that he is at east one of these two things. So David belongs to the set M U T exactly in the same way as all students that are at least one of these two things : math student OR tennis player.



    The OR that defines the union operation is inclusive.






    share|cite|improve this answer












    $endgroup$











    • 2




      $begingroup$
      Well, at my university the president is a woman.
      $endgroup$
      – Michael
      May 28 at 17:04



















    2
















    $begingroup$

    The union of two sets $A,B$ is defined by the ''or'' operation in propositional logic:
    $$Acup B = {xmid xin Avee xin B}.$$






    share|cite|improve this answer










    $endgroup$























      1
















      $begingroup$

      A U B are all the elements of set A and set B. Read as 'A or B' (A union B).
      Whereas,
      A Π B are all the elements which set A and set B have in common. Read as 'A intersection B' (A and B).






      share|cite|improve this answer












      $endgroup$















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        Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
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      5 Answers
      5






      active

      oldest

      votes








      5 Answers
      5






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      5
















      $begingroup$

      Because the elements of $A cup B$ are exactly those objects that belong to $A$ or belong to $B$.






      share|cite|improve this answer










      $endgroup$











      • 1




        $begingroup$
        I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
        $endgroup$
        – nuala
        May 28 at 21:12


















      5
















      $begingroup$

      Because the elements of $A cup B$ are exactly those objects that belong to $A$ or belong to $B$.






      share|cite|improve this answer










      $endgroup$











      • 1




        $begingroup$
        I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
        $endgroup$
        – nuala
        May 28 at 21:12
















      5














      5










      5







      $begingroup$

      Because the elements of $A cup B$ are exactly those objects that belong to $A$ or belong to $B$.






      share|cite|improve this answer










      $endgroup$



      Because the elements of $A cup B$ are exactly those objects that belong to $A$ or belong to $B$.







      share|cite|improve this answer













      share|cite|improve this answer




      share|cite|improve this answer










      answered May 28 at 12:30









      Mauro ALLEGRANZAMauro ALLEGRANZA

      71.8k5 gold badges51 silver badges122 bronze badges




      71.8k5 gold badges51 silver badges122 bronze badges











      • 1




        $begingroup$
        I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
        $endgroup$
        – nuala
        May 28 at 21:12
















      • 1




        $begingroup$
        I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
        $endgroup$
        – nuala
        May 28 at 21:12










      1




      1




      $begingroup$
      I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
      $endgroup$
      – nuala
      May 28 at 21:12






      $begingroup$
      I'd like to add [from my limited knowledge] an "or" mostly means an 'inclusive or' [x being in A or in B or even in both [A and B], like stated in the question "and/or"] as opposed to an 'exclusive or' (or XOR) where x shall be in A or B but not in both! en.wikipedia.org/wiki/Exclusive_or
      $endgroup$
      – nuala
      May 28 at 21:12















      3
















      $begingroup$

      The claim "$p$ or $q$" is true if either $p$ is true, or $q$ is true, or $p$ and $q$ are both true.



      That is, the claim "I am human or I am over one meter tall" is true, because at least one of the subclaims is true (in this case, both are true)






      share|cite|improve this answer










      $endgroup$




















        3
















        $begingroup$

        The claim "$p$ or $q$" is true if either $p$ is true, or $q$ is true, or $p$ and $q$ are both true.



        That is, the claim "I am human or I am over one meter tall" is true, because at least one of the subclaims is true (in this case, both are true)






        share|cite|improve this answer










        $endgroup$


















          3














          3










          3







          $begingroup$

          The claim "$p$ or $q$" is true if either $p$ is true, or $q$ is true, or $p$ and $q$ are both true.



          That is, the claim "I am human or I am over one meter tall" is true, because at least one of the subclaims is true (in this case, both are true)






          share|cite|improve this answer










          $endgroup$



          The claim "$p$ or $q$" is true if either $p$ is true, or $q$ is true, or $p$ and $q$ are both true.



          That is, the claim "I am human or I am over one meter tall" is true, because at least one of the subclaims is true (in this case, both are true)







          share|cite|improve this answer













          share|cite|improve this answer




          share|cite|improve this answer










          answered May 28 at 12:30









          5xum5xum

          97.6k5 gold badges101 silver badges168 bronze badges




          97.6k5 gold badges101 silver badges168 bronze badges


























              3
















              $begingroup$

              Suppose we are in a university.



              The President orders ( for some reason we do not care about) the following thing: I want all math students and all students that play tennis to be present in the great hall tomorrow ( and no other person).



              The next day, due to the strong authority of the President, all math students and all students playing tennis are present in the great hall.



              Certainly, the President has in front of him all the members of the set : M U T ( that is the union of set M and of set T)



              with M = the set of all math students
              and T = the set of students playing tennis.



              Now, what does the President know of any one of the students present there ( although he has possibly never met anyone of these students before)?



              For example, what does the President know about David, one of the students that is there?



              The only thing he knows for sure is that :



              David is a math student OR David is a student that plays tennis.



              Remark : of course, it could be the case David to be both a math student and a tennis player; but of this, the President has absolutely not idea.



              In other words he only knows for sure that : one at least of these two propositions is true :



              (1) David is a math student



              (2) David is a student that plays tennis



              and this " at least one" is precisely what defines the inclusive OR operator in logic.



              Since the same thing could be said about any student, one can say in general that :



              The set : M U T is the set of all x such that (1) x is a math student OR (2) x is a student that plays tennis.



              In symbols : M U T = { x | x belongs to M v x belongs to T }



              You might say : but there are certainly students in the hall that both are maths students and play tennis.



              You would be right, but notice that if a student, say, David is both a math student and a tennis player, this is precisely an excellent reason to say that he is at east one of these two things. So David belongs to the set M U T exactly in the same way as all students that are at least one of these two things : math student OR tennis player.



              The OR that defines the union operation is inclusive.






              share|cite|improve this answer












              $endgroup$











              • 2




                $begingroup$
                Well, at my university the president is a woman.
                $endgroup$
                – Michael
                May 28 at 17:04
















              3
















              $begingroup$

              Suppose we are in a university.



              The President orders ( for some reason we do not care about) the following thing: I want all math students and all students that play tennis to be present in the great hall tomorrow ( and no other person).



              The next day, due to the strong authority of the President, all math students and all students playing tennis are present in the great hall.



              Certainly, the President has in front of him all the members of the set : M U T ( that is the union of set M and of set T)



              with M = the set of all math students
              and T = the set of students playing tennis.



              Now, what does the President know of any one of the students present there ( although he has possibly never met anyone of these students before)?



              For example, what does the President know about David, one of the students that is there?



              The only thing he knows for sure is that :



              David is a math student OR David is a student that plays tennis.



              Remark : of course, it could be the case David to be both a math student and a tennis player; but of this, the President has absolutely not idea.



              In other words he only knows for sure that : one at least of these two propositions is true :



              (1) David is a math student



              (2) David is a student that plays tennis



              and this " at least one" is precisely what defines the inclusive OR operator in logic.



              Since the same thing could be said about any student, one can say in general that :



              The set : M U T is the set of all x such that (1) x is a math student OR (2) x is a student that plays tennis.



              In symbols : M U T = { x | x belongs to M v x belongs to T }



              You might say : but there are certainly students in the hall that both are maths students and play tennis.



              You would be right, but notice that if a student, say, David is both a math student and a tennis player, this is precisely an excellent reason to say that he is at east one of these two things. So David belongs to the set M U T exactly in the same way as all students that are at least one of these two things : math student OR tennis player.



              The OR that defines the union operation is inclusive.






              share|cite|improve this answer












              $endgroup$











              • 2




                $begingroup$
                Well, at my university the president is a woman.
                $endgroup$
                – Michael
                May 28 at 17:04














              3














              3










              3







              $begingroup$

              Suppose we are in a university.



              The President orders ( for some reason we do not care about) the following thing: I want all math students and all students that play tennis to be present in the great hall tomorrow ( and no other person).



              The next day, due to the strong authority of the President, all math students and all students playing tennis are present in the great hall.



              Certainly, the President has in front of him all the members of the set : M U T ( that is the union of set M and of set T)



              with M = the set of all math students
              and T = the set of students playing tennis.



              Now, what does the President know of any one of the students present there ( although he has possibly never met anyone of these students before)?



              For example, what does the President know about David, one of the students that is there?



              The only thing he knows for sure is that :



              David is a math student OR David is a student that plays tennis.



              Remark : of course, it could be the case David to be both a math student and a tennis player; but of this, the President has absolutely not idea.



              In other words he only knows for sure that : one at least of these two propositions is true :



              (1) David is a math student



              (2) David is a student that plays tennis



              and this " at least one" is precisely what defines the inclusive OR operator in logic.



              Since the same thing could be said about any student, one can say in general that :



              The set : M U T is the set of all x such that (1) x is a math student OR (2) x is a student that plays tennis.



              In symbols : M U T = { x | x belongs to M v x belongs to T }



              You might say : but there are certainly students in the hall that both are maths students and play tennis.



              You would be right, but notice that if a student, say, David is both a math student and a tennis player, this is precisely an excellent reason to say that he is at east one of these two things. So David belongs to the set M U T exactly in the same way as all students that are at least one of these two things : math student OR tennis player.



              The OR that defines the union operation is inclusive.






              share|cite|improve this answer












              $endgroup$



              Suppose we are in a university.



              The President orders ( for some reason we do not care about) the following thing: I want all math students and all students that play tennis to be present in the great hall tomorrow ( and no other person).



              The next day, due to the strong authority of the President, all math students and all students playing tennis are present in the great hall.



              Certainly, the President has in front of him all the members of the set : M U T ( that is the union of set M and of set T)



              with M = the set of all math students
              and T = the set of students playing tennis.



              Now, what does the President know of any one of the students present there ( although he has possibly never met anyone of these students before)?



              For example, what does the President know about David, one of the students that is there?



              The only thing he knows for sure is that :



              David is a math student OR David is a student that plays tennis.



              Remark : of course, it could be the case David to be both a math student and a tennis player; but of this, the President has absolutely not idea.



              In other words he only knows for sure that : one at least of these two propositions is true :



              (1) David is a math student



              (2) David is a student that plays tennis



              and this " at least one" is precisely what defines the inclusive OR operator in logic.



              Since the same thing could be said about any student, one can say in general that :



              The set : M U T is the set of all x such that (1) x is a math student OR (2) x is a student that plays tennis.



              In symbols : M U T = { x | x belongs to M v x belongs to T }



              You might say : but there are certainly students in the hall that both are maths students and play tennis.



              You would be right, but notice that if a student, say, David is both a math student and a tennis player, this is precisely an excellent reason to say that he is at east one of these two things. So David belongs to the set M U T exactly in the same way as all students that are at least one of these two things : math student OR tennis player.



              The OR that defines the union operation is inclusive.







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              edited May 29 at 16:14

























              answered May 28 at 14:59









              Eleonore Saint JamesEleonore Saint James

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              • 2




                $begingroup$
                Well, at my university the president is a woman.
                $endgroup$
                – Michael
                May 28 at 17:04














              • 2




                $begingroup$
                Well, at my university the president is a woman.
                $endgroup$
                – Michael
                May 28 at 17:04








              2




              2




              $begingroup$
              Well, at my university the president is a woman.
              $endgroup$
              – Michael
              May 28 at 17:04




              $begingroup$
              Well, at my university the president is a woman.
              $endgroup$
              – Michael
              May 28 at 17:04











              2
















              $begingroup$

              The union of two sets $A,B$ is defined by the ''or'' operation in propositional logic:
              $$Acup B = {xmid xin Avee xin B}.$$






              share|cite|improve this answer










              $endgroup$




















                2
















                $begingroup$

                The union of two sets $A,B$ is defined by the ''or'' operation in propositional logic:
                $$Acup B = {xmid xin Avee xin B}.$$






                share|cite|improve this answer










                $endgroup$


















                  2














                  2










                  2







                  $begingroup$

                  The union of two sets $A,B$ is defined by the ''or'' operation in propositional logic:
                  $$Acup B = {xmid xin Avee xin B}.$$






                  share|cite|improve this answer










                  $endgroup$



                  The union of two sets $A,B$ is defined by the ''or'' operation in propositional logic:
                  $$Acup B = {xmid xin Avee xin B}.$$







                  share|cite|improve this answer













                  share|cite|improve this answer




                  share|cite|improve this answer










                  answered May 28 at 12:31









                  WuestenfuxWuestenfux

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                      1
















                      $begingroup$

                      A U B are all the elements of set A and set B. Read as 'A or B' (A union B).
                      Whereas,
                      A Π B are all the elements which set A and set B have in common. Read as 'A intersection B' (A and B).






                      share|cite|improve this answer












                      $endgroup$















                      • $begingroup$
                        Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
                        $endgroup$
                        – dantopa
                        May 28 at 15:36
















                      1
















                      $begingroup$

                      A U B are all the elements of set A and set B. Read as 'A or B' (A union B).
                      Whereas,
                      A Π B are all the elements which set A and set B have in common. Read as 'A intersection B' (A and B).






                      share|cite|improve this answer












                      $endgroup$















                      • $begingroup$
                        Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
                        $endgroup$
                        – dantopa
                        May 28 at 15:36














                      1














                      1










                      1







                      $begingroup$

                      A U B are all the elements of set A and set B. Read as 'A or B' (A union B).
                      Whereas,
                      A Π B are all the elements which set A and set B have in common. Read as 'A intersection B' (A and B).






                      share|cite|improve this answer












                      $endgroup$



                      A U B are all the elements of set A and set B. Read as 'A or B' (A union B).
                      Whereas,
                      A Π B are all the elements which set A and set B have in common. Read as 'A intersection B' (A and B).







                      share|cite|improve this answer















                      share|cite|improve this answer




                      share|cite|improve this answer








                      edited May 30 at 15:06

























                      answered May 28 at 15:17









                      Harshit BhardwajHarshit Bhardwaj

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                        – dantopa
                        May 28 at 15:36


















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                        – dantopa
                        May 28 at 15:36
















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                      May 28 at 15:36




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                      Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
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                      May 28 at 15:36



















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