For each of 5-21 prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A and B, P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set ∪.

For all sets A and B, P(A∩B)=P(A)∩P(B)

Given information:

Let  A and B  be any set

Concept used:

∪:Union of sets∩:Intersection of sets

⊆: subset of set

Calculation:

Let A and B be subsets of a universal set U.

The objective is to prove whether the following statement is true or not else provide a counter example.

For all sets A and B.

P(A∩B)=P(A)∩P(B)

Let x∈P(A∩B)

By the definition of power set