Question

prove that AUB = AU(B\A)

Answer 1

$A ∪ (B − A) = A ∪ (B ∩ A^C)$ set difference

$= A ∪ (A^C ∩ B)$ commutative

$= (A ∪ A^C) ∩ (A ∪ B)$   distributive

$= U ∩ (A ∪ B)$ complement

$= A ∪ B$ identity