For any two sets A and B, prove that (A ∪ B) – B = A – B
(A ∪ B) – B = A – B
Let us consider LHS (A ∪ B) – B
= (A–B) ∪ (B–B)
= (A–B) ∪ ϕ (since, B–B = ϕ)
= A–B (since, x ∪ ϕ = x for any set)
= RHS
Hence proved.
If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.
Prove that A – B = A ∩ B.’
Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.
Prove that A ∩ (A ⋃ B)’ = ϕ
If A = {3, {2}}, find P(A).