Question 10
Let A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}. Find A\(B\C) and (A\B)\C. What can we conclude about set difference operation?
Solution:
A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}
L.H.S
A\(B\C)
(B\C) = {-2,-1,0} \ {-6,-4,-2}
= {-1,0}
A\(B\C) = {-5,-3,-2,-1} \ {-1,0}
= {-5,-3,-2} ---- (1)
R.H.S
(A\B)\C
(A\B) = {-5,-3,-2,-1} \ {-2,-1,0}
= {-5,-3}
(A\B)\C = {-5,-3} \ {-6,-4,-2}
= {-5,-3} -----(2)
(1) ≠ (2)
A\(B\C) ≠ (A\B)\C