Is a $S$ an element or subset or both of $T$? [closed]

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I have a question on basic set theory.



$S = a, b$

$T= a, b, c, d, e, f $



  1. Is $S$ a subset of $T$?

  2. Is $S$ an element of $T$?






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closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
If this question can be reworded to fit the rules in the help center, please edit the question.












  • $S$ is a subset of $T$, and is not an element of $T$. Do you see why?
    – Suzet
    Aug 1 at 11:31











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 11:32










  • I don't understand how $a,b$ is an incorrect formatting of a,b.
    – Asaf Karagila
    Aug 1 at 11:36






  • 1




    Did you though?
    – Asaf Karagila
    Aug 1 at 11:38






  • 1




    Ryan. I can help you, sure. But first I need to you settle on a version of the question.
    – Asaf Karagila
    Aug 1 at 11:42














up vote
-2
down vote

favorite
1












I have a question on basic set theory.



$S = a, b$

$T= a, b, c, d, e, f $



  1. Is $S$ a subset of $T$?

  2. Is $S$ an element of $T$?






share|cite|improve this question













closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
If this question can be reworded to fit the rules in the help center, please edit the question.












  • $S$ is a subset of $T$, and is not an element of $T$. Do you see why?
    – Suzet
    Aug 1 at 11:31











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 11:32










  • I don't understand how $a,b$ is an incorrect formatting of a,b.
    – Asaf Karagila
    Aug 1 at 11:36






  • 1




    Did you though?
    – Asaf Karagila
    Aug 1 at 11:38






  • 1




    Ryan. I can help you, sure. But first I need to you settle on a version of the question.
    – Asaf Karagila
    Aug 1 at 11:42












up vote
-2
down vote

favorite
1









up vote
-2
down vote

favorite
1






1





I have a question on basic set theory.



$S = a, b$

$T= a, b, c, d, e, f $



  1. Is $S$ a subset of $T$?

  2. Is $S$ an element of $T$?






share|cite|improve this question













I have a question on basic set theory.



$S = a, b$

$T= a, b, c, d, e, f $



  1. Is $S$ a subset of $T$?

  2. Is $S$ an element of $T$?








share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 1 at 11:48









Asaf Karagila

291k31401731




291k31401731









asked Aug 1 at 11:29







user580935











closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Mauro ALLEGRANZA, Batominovski, Simply Beautiful Art, John Ma, Isaac Browne Aug 1 at 17:05


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Batominovski, Simply Beautiful Art, John Ma, Isaac Browne
If this question can be reworded to fit the rules in the help center, please edit the question.











  • $S$ is a subset of $T$, and is not an element of $T$. Do you see why?
    – Suzet
    Aug 1 at 11:31











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 11:32










  • I don't understand how $a,b$ is an incorrect formatting of a,b.
    – Asaf Karagila
    Aug 1 at 11:36






  • 1




    Did you though?
    – Asaf Karagila
    Aug 1 at 11:38






  • 1




    Ryan. I can help you, sure. But first I need to you settle on a version of the question.
    – Asaf Karagila
    Aug 1 at 11:42
















  • $S$ is a subset of $T$, and is not an element of $T$. Do you see why?
    – Suzet
    Aug 1 at 11:31











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 11:32










  • I don't understand how $a,b$ is an incorrect formatting of a,b.
    – Asaf Karagila
    Aug 1 at 11:36






  • 1




    Did you though?
    – Asaf Karagila
    Aug 1 at 11:38






  • 1




    Ryan. I can help you, sure. But first I need to you settle on a version of the question.
    – Asaf Karagila
    Aug 1 at 11:42















$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31





$S$ is a subset of $T$, and is not an element of $T$. Do you see why?
– Suzet
Aug 1 at 11:31













Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 11:32












I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36




I don't understand how $a,b$ is an incorrect formatting of a,b.
– Asaf Karagila
Aug 1 at 11:36




1




1




Did you though?
– Asaf Karagila
Aug 1 at 11:38




Did you though?
– Asaf Karagila
Aug 1 at 11:38




1




1




Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42




Ryan. I can help you, sure. But first I need to you settle on a version of the question.
– Asaf Karagila
Aug 1 at 11:42










4 Answers
4






active

oldest

votes

















up vote
1
down vote



accepted










The easy way to solve these questions is to put dummy variables.



This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.



Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?






share|cite|improve this answer




























    up vote
    1
    down vote













    $S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.



    $S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.






    share|cite|improve this answer

















    • 2




      This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
      – Henning Makholm
      Aug 1 at 11:46

















    up vote
    0
    down vote













    No and no, because $a neq a$ and $b neq b$.



    To (i): It is



    $$a, b subset T,$$



    but



    $$a, b notsubset T.$$



    To (ii): It is



    $$a in T text and b in T, $$



    but



    $$ a,b notin T. $$






    share|cite|improve this answer




























      up vote
      0
      down vote













      Edit : Since the question had two different versions, I'm gonna reply to both.



      Case where $S = a,b$ :

      $S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.




      Case where $S = a,b$ :

      $S$ is a subset of $T$ since all elements of $S$ are elements of $T$.

      $S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.






      share|cite|improve this answer



















      • 2




        "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
        – Henning Makholm
        Aug 1 at 11:43











      • But doesn't my example in parenthesis resolves the ambiguity ?
        – Pakos
        Aug 1 at 11:56
















      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      1
      down vote



      accepted










      The easy way to solve these questions is to put dummy variables.



      This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.



      Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?






      share|cite|improve this answer

























        up vote
        1
        down vote



        accepted










        The easy way to solve these questions is to put dummy variables.



        This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.



        Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?






        share|cite|improve this answer























          up vote
          1
          down vote



          accepted







          up vote
          1
          down vote



          accepted






          The easy way to solve these questions is to put dummy variables.



          This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.



          Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?






          share|cite|improve this answer













          The easy way to solve these questions is to put dummy variables.



          This is just like how $(x^4+5234-sqrt x)^2=3$ is easier to solve when setting $t=x^4+5234-sqrt x$, and thus $t^2=3$, it is sometimes easier to solve these problems when you replace the inner sets with dummy variables.



          Set $x=a,y=b,z=c,w=d,e,f$. Now we have $S=x,y$ and $T=x,y,z,w$. Which one is true now, is $Sin T$ or $Ssubseteq T$, or both?







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered Aug 1 at 11:46









          Asaf Karagila

          291k31401731




          291k31401731




















              up vote
              1
              down vote













              $S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.



              $S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.






              share|cite|improve this answer

















              • 2




                This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
                – Henning Makholm
                Aug 1 at 11:46














              up vote
              1
              down vote













              $S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.



              $S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.






              share|cite|improve this answer

















              • 2




                This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
                – Henning Makholm
                Aug 1 at 11:46












              up vote
              1
              down vote










              up vote
              1
              down vote









              $S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.



              $S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.






              share|cite|improve this answer













              $S$ is not a subset of $T$, otherwise we would have $a in T$, which is not the case.



              $S$ is not an element of $T$, otherwise we would have $a,b in T$, which is not the case.







              share|cite|improve this answer













              share|cite|improve this answer



              share|cite|improve this answer











              answered Aug 1 at 11:41









              Fred

              37k1237




              37k1237







              • 2




                This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
                – Henning Makholm
                Aug 1 at 11:46












              • 2




                This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
                – Henning Makholm
                Aug 1 at 11:46







              2




              2




              This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
              – Henning Makholm
              Aug 1 at 11:46




              This was a correct answer when it was posted -- a few minutes later the OP changed the question once again ...
              – Henning Makholm
              Aug 1 at 11:46










              up vote
              0
              down vote













              No and no, because $a neq a$ and $b neq b$.



              To (i): It is



              $$a, b subset T,$$



              but



              $$a, b notsubset T.$$



              To (ii): It is



              $$a in T text and b in T, $$



              but



              $$ a,b notin T. $$






              share|cite|improve this answer

























                up vote
                0
                down vote













                No and no, because $a neq a$ and $b neq b$.



                To (i): It is



                $$a, b subset T,$$



                but



                $$a, b notsubset T.$$



                To (ii): It is



                $$a in T text and b in T, $$



                but



                $$ a,b notin T. $$






                share|cite|improve this answer























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  No and no, because $a neq a$ and $b neq b$.



                  To (i): It is



                  $$a, b subset T,$$



                  but



                  $$a, b notsubset T.$$



                  To (ii): It is



                  $$a in T text and b in T, $$



                  but



                  $$ a,b notin T. $$






                  share|cite|improve this answer













                  No and no, because $a neq a$ and $b neq b$.



                  To (i): It is



                  $$a, b subset T,$$



                  but



                  $$a, b notsubset T.$$



                  To (ii): It is



                  $$a in T text and b in T, $$



                  but



                  $$ a,b notin T. $$







                  share|cite|improve this answer













                  share|cite|improve this answer



                  share|cite|improve this answer











                  answered Aug 1 at 11:46









                  til

                  694




                  694




















                      up vote
                      0
                      down vote













                      Edit : Since the question had two different versions, I'm gonna reply to both.



                      Case where $S = a,b$ :

                      $S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.




                      Case where $S = a,b$ :

                      $S$ is a subset of $T$ since all elements of $S$ are elements of $T$.

                      $S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.






                      share|cite|improve this answer



















                      • 2




                        "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                        – Henning Makholm
                        Aug 1 at 11:43











                      • But doesn't my example in parenthesis resolves the ambiguity ?
                        – Pakos
                        Aug 1 at 11:56














                      up vote
                      0
                      down vote













                      Edit : Since the question had two different versions, I'm gonna reply to both.



                      Case where $S = a,b$ :

                      $S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.




                      Case where $S = a,b$ :

                      $S$ is a subset of $T$ since all elements of $S$ are elements of $T$.

                      $S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.






                      share|cite|improve this answer



















                      • 2




                        "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                        – Henning Makholm
                        Aug 1 at 11:43











                      • But doesn't my example in parenthesis resolves the ambiguity ?
                        – Pakos
                        Aug 1 at 11:56












                      up vote
                      0
                      down vote










                      up vote
                      0
                      down vote









                      Edit : Since the question had two different versions, I'm gonna reply to both.



                      Case where $S = a,b$ :

                      $S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.




                      Case where $S = a,b$ :

                      $S$ is a subset of $T$ since all elements of $S$ are elements of $T$.

                      $S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.






                      share|cite|improve this answer















                      Edit : Since the question had two different versions, I'm gonna reply to both.



                      Case where $S = a,b$ :

                      $S$ would have been a subset of T if the elements $a$ and $b$ were contained in $T$ (example : $T = a,b,c,d,e,f,a,b$), and $S$ would have been an element of $T$ if... Well, if a,b was an element of T (example : $T = a,b,c,d,e,f,a,b$), so $S$ is neither a subset nor an element of $T$.




                      Case where $S = a,b$ :

                      $S$ is a subset of $T$ since all elements of $S$ are elements of $T$.

                      $S$ would have been an element of $T$ if the element $a,b$ was an element of $T$.







                      share|cite|improve this answer















                      share|cite|improve this answer



                      share|cite|improve this answer








                      edited Aug 1 at 11:54


























                      answered Aug 1 at 11:39









                      Pakos

                      11




                      11







                      • 2




                        "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                        – Henning Makholm
                        Aug 1 at 11:43











                      • But doesn't my example in parenthesis resolves the ambiguity ?
                        – Pakos
                        Aug 1 at 11:56












                      • 2




                        "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                        – Henning Makholm
                        Aug 1 at 11:43











                      • But doesn't my example in parenthesis resolves the ambiguity ?
                        – Pakos
                        Aug 1 at 11:56







                      2




                      2




                      "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                      – Henning Makholm
                      Aug 1 at 11:43





                      "Contained in" is not good wording to use in an explanation for a confused beginner, because that wording is used both for subsets and for elements, by people who trust their audience can resolve the ambiguity on their own.
                      – Henning Makholm
                      Aug 1 at 11:43













                      But doesn't my example in parenthesis resolves the ambiguity ?
                      – Pakos
                      Aug 1 at 11:56




                      But doesn't my example in parenthesis resolves the ambiguity ?
                      – Pakos
                      Aug 1 at 11:56


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