Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the identities A – (B ∪ C) = (A – B) ∩ (A – C)

A – (B ∪ C) = (A – B) ∩ (A – C)

Firstly let us consider the LHS

(B ∪ C) = {x: x ∈ B or x ∈ C}

= {2, 3, 4, 5, 6, 7}.

A – (B ∪ C) is defined as {x ∈ A: x ∉ (B ∪ C)}

A = {1, 2, 4, 5}

(B ∪ C) = {2, 3, 4, 5, 6, 7}

A – (B ∪ C) = {1}

Now, RHS

(A – B)

A – B is defined as {x ∈ A: x ∉ B}

A = {1, 2, 4, 5}

B = {2, 3, 5, 6}

A – B = {1, 4}

(A – C)

A – C is defined as {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)}.

= {1}

LHS = RHS

Hence verified.