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)."

(Headbang)

Thanks for helping in advance

Printable View

- Aug 30th 2009, 08:32 AMfaisalnet5Prove 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)."

(Headbang)

Thanks for helping in advance - Aug 30th 2009, 08:47 AMPlato
Consider two cases.

1) If $\displaystyle C \in \mathcal{P}(A \cup B)$ is it true that $\displaystyle C \in \mathcal{P}(A)$ or $\displaystyle C \in \mathcal{P}(B)$

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

If both of those are true the they are equal.

Otherwise, find a simple counter-example.