Using properties of sets show that(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.
Answer»
(i) To show: A ∪ (A ∩ B) = A We know that A ⊂ A A ∩ B ⊂ A ∴ A ∪ (A ∩ B) ⊂ A … (1) Also, A ⊂ A ∪ (A ∩ B) … (2) ∴ From (1) and (2), A ∪ (A ∩ B) = A (ii) To show: A ∩ (A ∪ B) = A A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B) = A ∪ (A ∩ B) = A {from (1)}