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Why would {a,b} be a subset?

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data


    Let A = {a,b}, find P(A), the power set which contains all subsets of A

    Soln:

    P(A) = {empty set, {a}, {b}, {a,b}}

    Why is {a,b} in there? Isn't that an element? Shouldn't it be {{a,b}}

    So

    P(A) = {es, {a}, {b}, {{a,b}}}?
     
  2. jcsd
  3. Sep 10, 2011 #2

    gb7nash

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    Yes. {a,b} is an element of P(A). That is, the set consisting of a and b is an element. Likewise, the set consisting of a is an element, the set consisting of b is an element.
     
  4. Sep 10, 2011 #3
    No, why?
    A is a subset of B if and only if [itex]A\subseteq B[/itex].
    Since {a,b} = {a,b} (do you agree? :tongue2:), {a,b}[itex]\subseteq[/itex]{a,b}, and therefore, {a,b} is a subset of {a,b}.

    (that is of course true generally: [itex]A\subseteq A[/itex] so [itex]A\in P(A)[/itex])

    However, {{a,b}} doesn't hold this relation.
     
  5. Sep 10, 2011 #4

    vela

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    The set A has two elements, a and b. That's it.

    {a}, {b}, and {a,b} are subsets of A, not elements of A.
     
  6. Sep 10, 2011 #5
    Yeah not following that logic at all lol
     
  7. Sep 10, 2011 #6
    What aren't you following?
     
  8. Sep 10, 2011 #7
    You know what, I got confused with another problem with this one. That problem had 1 nonset element and all the others are.

    Thank you everyone
     
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