Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the

1.	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)
Answer» (B ∩ C) = {x:x ϵ B and x ϵ C} = {5, 6} (A – (B ∩ C)) = A–(B ∩ C) is defined as {x ϵ A : x ∉(B ∩ C)} A = {1, 2, 4, 5} (B ∩ C) = {5, 6} (A – (B ∩ C)) = {1, 2, 4} 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) OR x ϵ (A – C) }. = {1, 2, 4} 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)

Answer»

(B ∩ C) = {x:x ϵ B and x ϵ C}

= {5, 6}

(A – (B ∩ C)) =

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

A = {1, 2, 4, 5}

(B ∩ C) = {5, 6}

(A – (B ∩ C)) = {1, 2, 4}

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) OR x ϵ (A – C) }.

= {1, 2, 4}

Hence verified