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