Question

Using Venn diagram verify the relation,
(A-B) U (A-C) = A - ( B ⋂ C)​

Answer 1

Explanation:

Let A, B, and C be three sets. Prove that A-(BUC) = (A-B) ∩ (A-C)

Solution)

L.H.S = A - (B U C)

A ∩ (B U C)c

A ∩ (B c ∩ Cc)

(A ∩ Bc) ∩ (A∩ Cc)

(AUB) ∩ (AUC)

R.H.S = (A-B) ∩ (A-C)

(A∩Bc) ∩ (A∩Cc)

(AUB) ∩ (AUC)

L.H.S = R.H.S