For any two sets A and B, prove the A ∩ (A‘ ∪ B) = A ∩ B
A ∩ (A’ ∪ B) = A ∩ B
Let us consider LHS A ∩ (A’ ∪ B)
Expanding
(A ∩ A’) ∪ (A ∩ B)
We know, (A ∩ A’) =ϕ
⇒ ϕ ∪ (A∩ B)
⇒ (A ∩ B)
LHS = 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).