Question

If A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 8}, C = {2, 5, 7, 8}, verify that A– (B U C) = (A–B) ∩ (A –C).

Answer 1

Answer:

(BUC) ={1,3,5,8}U{2,5,7,8}

={1,2,3,5,7,8}

A-(BUC)={1,2,3,4,5}-{1,2,3,5,7,8}

={4}

(A-B) ={1,2,3,4,5}-{1,3,5,8}

={2,4}

(A-C)={1,2,3,4,5}-{2,5,7,8}

={1,3,4}

(A-B) U(A-C) ={2,4} U {1,3,4}

={1,2,3,4}

THEREFORE A-(BUC) is not equal to (A-B) U(A-C)

Answer 2

Answer:

BUC={1,3,5,8}U{2,5,7,8}={1,2,3,5,7,8}

A-(BUC)={1,2,3,4,5}-{1,2,3,5,7,8}={4}=L.H.S

A-B={1,2,3,4,5}-{1,3,5,8}={2,4}

A-C={1,2,3,4,5}-{2,5,7,8}={1,3,4}

(A-B)∩(A-C)={2,4}∩{1,3,4}={4}=R.H.S