The number of possible subsets of the set {1,{3,4}}?












-1












$begingroup$


I found this question in an exam and my answer was 8(=2^3) which was evaluated as wrong. Can anyone provide their inputs on the why the no. of subsets is only 4 where as the number of elements is 3.



Thanks.






elementary-set-theory







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  • 2




    $begingroup$
    Note that {3,4} is a single element , not 2.
    $endgroup$
    – Sinπ
    Jan 14 at 8:13












  • $begingroup$
    You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
    $endgroup$
    – 5xum
    Jan 15 at 8:51
















-1












$begingroup$


I found this question in an exam and my answer was 8(=2^3) which was evaluated as wrong. Can anyone provide their inputs on the why the no. of subsets is only 4 where as the number of elements is 3.



Thanks.






elementary-set-theory







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    Note that {3,4} is a single element , not 2.
    $endgroup$
    – Sinπ
    Jan 14 at 8:13












  • $begingroup$
    You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
    $endgroup$
    – 5xum
    Jan 15 at 8:51














-1












-1








-1


0



$begingroup$


I found this question in an exam and my answer was 8(=2^3) which was evaluated as wrong. Can anyone provide their inputs on the why the no. of subsets is only 4 where as the number of elements is 3.



Thanks.






elementary-set-theory







share|cite|improve this question











$endgroup$




I found this question in an exam and my answer was 8(=2^3) which was evaluated as wrong. Can anyone provide their inputs on the why the no. of subsets is only 4 where as the number of elements is 3.



Thanks.






elementary-set-theory




elementary-set-theory






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share|cite|improve this question













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share|cite|improve this question








edited Jan 14 at 8:46









Asaf Karagila♦

307k33438769




307k33438769










asked Jan 14 at 8:11









Chenreddy SahithiChenreddy Sahithi

1




1








  • 2




    $begingroup$
    Note that {3,4} is a single element , not 2.
    $endgroup$
    – Sinπ
    Jan 14 at 8:13












  • $begingroup$
    You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
    $endgroup$
    – 5xum
    Jan 15 at 8:51














  • 2




    $begingroup$
    Note that {3,4} is a single element , not 2.
    $endgroup$
    – Sinπ
    Jan 14 at 8:13












  • $begingroup$
    You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
    $endgroup$
    – 5xum
    Jan 15 at 8:51








2




2




$begingroup$
Note that {3,4} is a single element , not 2.
$endgroup$
– Sinπ
Jan 14 at 8:13






$begingroup$
Note that {3,4} is a single element , not 2.
$endgroup$
– Sinπ
Jan 14 at 8:13














$begingroup$
You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
$endgroup$
– 5xum
Jan 15 at 8:51




$begingroup$
You recieved 2 answers to your question. Is any of them what you needed? If so, you should upvote all the useful answers and accept the answer that is most useful to you.
$endgroup$
– 5xum
Jan 15 at 8:51










2 Answers
2






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$begingroup$


  • If $A$ has $k$ elements, then the number of possible subsets of $A$ is $2^k$.

  • Your set has $2$ elements

  • Therefore, your set has $2^2=4$ possible subsets.


In particular, the $4$ subsets of your set are:



$$varnothing, {1}, {{3,4}}, {1,{3,4}}$$






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    One can consider the problem more abstractly by taking the set $A={a,b}$. It has the power set $2^A= {emptyset, {a},{b},{a,b}}$. In your case, $a=1$ and $b={3,4}$.






    share|cite|improve this answer











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      2 Answers
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      2 Answers
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      3












      $begingroup$


      • If $A$ has $k$ elements, then the number of possible subsets of $A$ is $2^k$.

      • Your set has $2$ elements

      • Therefore, your set has $2^2=4$ possible subsets.


      In particular, the $4$ subsets of your set are:



      $$varnothing, {1}, {{3,4}}, {1,{3,4}}$$






      share|cite|improve this answer









      $endgroup$


















        3












        $begingroup$


        • If $A$ has $k$ elements, then the number of possible subsets of $A$ is $2^k$.

        • Your set has $2$ elements

        • Therefore, your set has $2^2=4$ possible subsets.


        In particular, the $4$ subsets of your set are:



        $$varnothing, {1}, {{3,4}}, {1,{3,4}}$$






        share|cite|improve this answer









        $endgroup$
















          3












          3








          3





          $begingroup$


          • If $A$ has $k$ elements, then the number of possible subsets of $A$ is $2^k$.

          • Your set has $2$ elements

          • Therefore, your set has $2^2=4$ possible subsets.


          In particular, the $4$ subsets of your set are:



          $$varnothing, {1}, {{3,4}}, {1,{3,4}}$$






          share|cite|improve this answer









          $endgroup$




          • If $A$ has $k$ elements, then the number of possible subsets of $A$ is $2^k$.

          • Your set has $2$ elements

          • Therefore, your set has $2^2=4$ possible subsets.


          In particular, the $4$ subsets of your set are:



          $$varnothing, {1}, {{3,4}}, {1,{3,4}}$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 14 at 8:15









          5xum5xum

          91.5k394161




          91.5k394161























              1












              $begingroup$

              One can consider the problem more abstractly by taking the set $A={a,b}$. It has the power set $2^A= {emptyset, {a},{b},{a,b}}$. In your case, $a=1$ and $b={3,4}$.






              share|cite|improve this answer











              $endgroup$


















                1












                $begingroup$

                One can consider the problem more abstractly by taking the set $A={a,b}$. It has the power set $2^A= {emptyset, {a},{b},{a,b}}$. In your case, $a=1$ and $b={3,4}$.






                share|cite|improve this answer











                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  One can consider the problem more abstractly by taking the set $A={a,b}$. It has the power set $2^A= {emptyset, {a},{b},{a,b}}$. In your case, $a=1$ and $b={3,4}$.






                  share|cite|improve this answer











                  $endgroup$



                  One can consider the problem more abstractly by taking the set $A={a,b}$. It has the power set $2^A= {emptyset, {a},{b},{a,b}}$. In your case, $a=1$ and $b={3,4}$.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Jan 14 at 8:58

























                  answered Jan 14 at 8:56









                  WuestenfuxWuestenfux

                  5,2931513




                  5,2931513






























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