Power set of (A intersect B)=Power set of A intersect the power set of B

x is an element of D which is an element of the power set of (A intersect B). a subset of A and B must contain elements that are in both A and B so x must be an element of A and B. Since x is an element of A it must be contained in the power set of A and since x is in B it must also be in the power set of B

i think this wrong but im not sure how to fix it