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Power Sets

  1. Mar 22, 2006 #1
    How in the heck do i prove these:

    Prove whether the following equations are true for all sets. For each one that's not always true, try to prove that one side is a subset of the other, and give a counterexample to the other direction. If neither side must be a subset of the other, give a counterexample to both directions:

    let P(A) denote the power set of A

    a) P(A U B) = P(A) U P(B)
    b) P(A-B) = P(A) - P(B)
     
  2. jcsd
  3. Mar 22, 2006 #2

    0rthodontist

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    a. is not true. Think about it, try an example or two. The subset goes from right to left. To prove things like this, you assume x is an element of P(A) U P(B) and show that x must be an element of P(A U B).

    b. is also not true, the subset goes from left to right.
     
  4. Mar 22, 2006 #3
    for part (b) i dont think either side is a subset of each other because:

    let A = {1,2}
    B = {1,3}
    A-B = {2}

    P(A) = {0, 1, 2, {1,2}}
    P(B) = {0, 1, 3, {1,3}}
    P(A)-P(B) = {2, {1,2}}
    P(A-B) = {0, 2}

    they aren't equal and one isn't a subset of another.
     
  5. Mar 22, 2006 #4

    0rthodontist

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    Ah, you're right.
     
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