Properties of Intersection of Sets –
Let A, B, C be any sets, then –
(1) A ∩ B = B ∩ A (Commutative Law)
(2) (A ∩ B) ∩ C = A ∩ (B ∩ C) (Associative Law)
(3) A ⊆ B then A ∩ B = A
(4) For any sets A & B, we have A ∩ B ⊆ A and A ∩ B ⊆ B
(5) A ∩ ϕ = ϕ
(6) Distributive Law –
If A, B, and C are any three sets then,
(i) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
(ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Your second block of text...