# proof involving power sets, and intersection

• Oct 9th 2009, 01:19 PM
proof involving power sets, and intersection
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
• Oct 9th 2009, 01:25 PM
Matt Westwood
Quote:

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

Nope, looks right to me.

All you need to do is point out that the argument reverses.

Here's the thing proved in symbols:

Intersection of Power Sets - ProofWiki
• Jan 12th 2010, 02:29 PM
rr1964
An element of a Set a is an element of a subset of the powerset
Note the given wiki proof more carefully. Although x is an element of A intersection B, it is not an element of the power set of either nor their intersection. It is an element of a subset of the power set, yes, but not an element of the power set itself. A power set is a set containing all possible subsets of a given set. This really is confusing though, I know. The same concept can be applied in reverse in that although x is an element of the power set of a set, it is not an element of the set itself.