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?

The statement A (B C) can be rewritten as A (B C). Here we have find the compliment values of the two statements and compare the results.

That means we have to check the associative properties of compliment or difference operation

That is we have to check A (B C) = (A B) C or not

Here we are given

A = {- 5, - 3, - 2, - 1},

B = {- 2, - 1,0}

C = {- 6, - 4, - 2}

L.H.S

Here for easy solving we will split the statement A (B C) into two parts. First we find the difference between set B and C then the difference between set A and the result obtained form (BC).

So using the data given

(BC) = {- 2, - 1, 0} {- 6, - 4, - 2}

= {-1, 0}

A (B C) = {- 5, - 3, - 2, - 1} {-1, 0}

= {–5, –3, –2}…………..(i)

R.H.S.

Here for easy solving we will split the statement (A B) C into two parts. First we find the difference between set A and B then again the difference is to be found between result obtained form (AB) and C.

So

(A B) = {- 5, - 3, - 2, - 1} {- 2, - 1, 0}

= {-5,-3}

Now (A B) C = {-5,-3} {- 6, - 4, - 2}

= {-5,-3}……………(ii)

So from (i) and (ii) it’s clear that

L.H.S ≠ R.H.S

I.e. A (B C) ≠ (A B) C

So from the above statement it’s clear that the difference or the compliment operation of set is not associative.