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, if A ⊆ B then 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 U.

For all sets A and B if A⊆B then 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:

Consider the following statement,

If A⊆B then P(A)⊆P(B)

The objective is to verify whether the statement is true or not

Recall, the definition for a power set,

A power set is a set of all the subsets of a set.

Let A and B are two sets, then the power sets of A and B are defined by,

Let A and B are two subsets of a universal set U