Answers:

(i) 

LHS,

B–C = {x ∈ B: x ∉ C}

B = {2, 3, 5, 6}

C = {4, 5, 6, 7}

B–C = {2, 3}

(A ∩ (B – C)) = {x: x ∈ A and x ∈ (B – C)}

(A ∩ (B – C)) = {2}

RHS,

(A ∩ B) = {x: x ∈ A and x ∈ B}

(A ∩ B) = {2, 5}

(A ∩ C) = {x: x ∈ A and x ∈ C}

(A ∩ C) = {4, 5}

(A ∩ B) – (A ∩ C) = {x ∈ (A ∩ B): x ∉ (A ∩ C)}

(A ∩ B) – (A ∩ C) = {2}

∴ LHS = RHS

Thus, Verified.

(ii)

LHS,

(B ∪ C) = {x: x ∈ B or x ∈ C}

(B ∪ C) = {2, 3, 4, 5, 6, 7}.

A – (B ∪ C) = {x ∈ A: x ∉ (B ∪ C)}

A = {1, 2, 4, 5}

(B ∪ C) = {2, 3, 4, 5, 6, 7}

A – (B ∪ C) = {1}

RHS,

A – B = {x ∈ A: x ∉ B}

A = {1, 2, 4, 5}

B = {2, 3, 5, 6}

A – B = {1, 4}

A – C = {x ∈ A: x ∉ C}

A = {1, 2, 4, 5}

C = {4, 5, 6, 7}

A – C = {1, 2}

(A – B) ∩ (A – C) = {x: x ∈ (A – B) and x ∈ (A – C)}.

(A – B) ∩ (A – C) = {1}

∴ LHS = RHS

Thus, verified.