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