Question

A U(B - A) = A UB
prove the statement​

Answer 1

Step-by-step explanation:

Proof.

A ∪ (B − A) = A ∪ (B ∩ A

c

) set difference

= A ∪ (A

c ∩ B) commutative

= (A ∪ A

c

) ∩ (A ∪ B) distributive

= U ∩ (A ∪ B) complement

= A ∪ B identity

Proof. Let x ∈ A ∪ (B − A). Then x ∈ A or x ∈ (B − A) by definition of

union. So x ∈ B and x 6∈ A (by set difference). But x ∈ A by previous

statement, so x ∈ A or x ∈ B. By definition of union, x ∈ (A ∪ B).