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Math Help - Prove or Disprove

  1. #1
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    Prove or Disprove

    How should i answer following type of question?

    "For any set X, let P(X) denote the power set of X. Let A and B be arbitrary sets. Prove or Disprove: P(AuB)=P(A) u P(B)."



    Thanks for helping in advance
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  2. #2
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    Quote Originally Posted by faisalnet5 View Post
    How should i answer following type of question?
    "For any set X, let P(X) denote the power set of X. Let A and B be arbitrary sets. Prove or Disprove: P(AuB)=P(A) u P(B)."
    Consider two cases.
    1) If C \in \mathcal{P}(A \cup B) is it true that C \in \mathcal{P}(A) or C \in \mathcal{P}(B)

    2) If D \in (\mathcal{P}(A)\cup\mathcal{P}(B)) is it true that D \in \mathcal{P}(A \cup B).

    If both of those are true the they are equal.

    Otherwise, find a simple counter-example.
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