# Thread: relation between power sets

1. ## relation between power sets

Suppose that A and B are not disjoint sets. How is, P(A instersect B), the power set of A intersect B, related to P(A) intersect P(B)? Provide evidence for this conclusion.

I just...I have no idea what this is asking or how to figure it out.

2. Originally Posted by kiddopop
Suppose that A and B are not disjoint sets. How is, P(A instersect B), the power set of A intersect B, related to P(A) intersect P(B)? Provide evidence for this conclusion.
$\mathcal{P}(A\cap B)=\mathcal{P}(A)\cap\mathcal{P}(B)$
You must show that $X\in\mathcal{P}(A\cap B)$ if and only if $X\in(\mathcal{P}(A)\cap\mathcal{P}(B))$.

3. Originally Posted by Plato
$\mathcal{P}(A\cap B)=\mathcal{P}(A)\cap\mathcal{P}(B)$
You must show that $X\in\mathcal{P}(A\cap B)$ if and only if $X\in(\mathcal{P}(A)\cap\mathcal{P}(B))$.
how do i do that? i'm so lost.

4. Originally Posted by kiddopop
how do i do that? i'm so lost.
What does $X\in\mathcal{P}(A\cap B)$ mean?

5. Originally Posted by Plato
What does $X\in\mathcal{P}(A\cap B)$ mean?
that x is an element of the power set of A and B?

6. Originally Posted by kiddopop
that x is an element of the power set of A and B?
What does it mean to be a an element of the power set of A intersect B?
Let's say $T\in\mathcal{P}(S)$, then what does that imply about $T~\&~S$.