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, A ∩ ( A ∪ B ) = A .

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, A∩(A∪B)=A .,

Given information:

Let  A and B   be any set

Concept used:

∪:Union of sets∩:Intersection of sets

⊆: subset of set

Calculation:

The objective is to prove that A∩(A∪B)=A .

Let A and B any sets.

Suppose x∈A∩(A∪B) then x∈A and x∈A∪B .

That is x∈A and x∈A or x∈B