Question

Prove
A-(BUC)=(A-B) intersection (A-C)​

Answer 1

This is the Answer ✌️

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

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

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)cA ∩ (B c ∩ Cc)(A ∩ Bc) ∩ (A∩ Cc)(AUB) ∩ (AUC)R.H.S = (A-B) ∩ (A-C)

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)cA ∩ (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