For A = {5,10,15,20} B = {6,10,12,18,24} and C ={7,10,12,14,21,28} verify whether A\ (B\C) = (A\B)\C. Justify your answer.

Question 9

For A = {5,10,15,20} B = {6,10,12,18,24} and C ={7,10,12,14,21,28} verify whether A\ (B\C) = (A\B)\C. Justify your answer.

Solution:

A = {5,10,15,20}

B = {6,10,12,18,24}

C = {7,10,12,14,21,28}

L.H.S

A\(B\C)

(B\C) = {6,10,12,18,24} \ {7,10,12,14,21,28}

    = {6,18,24}

A\(B\C) = {5,10,15,20} \ {6,18,24}

       = {5,10,15,20}  ---(1)

(A\B) = {5,10,15,20}\{6,10,12,18,24}

    = {5,15,20}

(A\B)\C = {5,15,20} \ {7,10,12,14,21,28}

       = {5,15,20}   --- (2)

A\ (B\C) ≠ (A\B)\C