Show that A ∩ B = A ∩ C need not imply B = C.
Let us assume,
A = {0, 1}
B = {0, 2, 3}
And, C = {0, 4, 5}
According to the question,
A ∩ B = {0}
And,
A ∩ C = {0}
A ∩ B = A ∩ C = {0}
But,
2 ∈ B and 2 ∉ C
Therefore, B ≠ C
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).