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

Question

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

Philoid · Accepted Answer

L.H.S.

(B ∪ C) = {x: x ϵ B or x ϵ C }

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

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

A = {1, 2, 4, 5}

(B ∪ C) = {2, 3, 4, 5, 6, 7}.

A–(B ∪ C) = {1}

R.H.S

(A – B) =

A–B is defined as {x ϵ 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 ϵ A : x ∉ C}

A = {1, 2, 4, 5}

C = {4, 5, 6, 7}

A–C = {1, 2}

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

= {1, 2}

Hence verified.

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