If A = {4,6,7,8,9}, B = {2,4,6} and C = {1,2,3,4,5,6}, then find

(i) A ∪ (B ∩ C)

(ii) A ∩ (B ∪ C)

(iii) A (C B)

(i) Here first we will find the elements of the set (B C). As we now the intersection operation will give a set containing the common elements of both the sets. After that we will use union operation between A and the set of elements obtained from intersection operation of B and C to find the next set of element. We know that a union operation between two sets gives all the element present in sets.

We are given that A = {4, 6, 7, 8, 9},

B = {2, 4, 6}

C = {1, 2, 3, 4, 5, 6}

So

(B Ո C) = {2, 4, 6} ⋂ {1, 2, 3, 4, 5, 6}

= {2, 4, 6}

Now,

A ⋃ (B ⋂ C) = {4, 6, 7, 8, 9} ⋃ {2, 4, 6}

= {2, 4, 6, 7, 8, 9}

(ii) Here first we will find the union set i.e. (B ⋃ C) it will give a new set of elements which are common to both B and C after that we will find the intersection between set A and the set obtained from the union operation of B and C

We are given that A = {4, 6, 7, 8, 9},

B = {2, 4, 6}

C = {1, 2, 3, 4, 5, 6}

So (B ⋃ C) = {2, 4, 6} ⋃ {1, 2, 3, 4, 5, 6}

= {1, 2, 3, 4, 5, 6}

Now A ⋂ (B ⋃ C) = {4, 6, 7, 8, 9} ⋂ {1, 2, 3, 4, 5, 6}

= {4, 6}

(iii) Here we will solve the problem in two part. First we will find the difference set CB which gives the element that are only a part of set C and doesn’t exist in set B after that we will find the difference between set A and the element obtained from (C B).

We are given that A = {4, 6, 7, 8, 9},

B = {2, 4, 6}

C = {1, 2, 3, 4, 5, 6}

So CB = {1, 2, 3, 4, 5, 6} {2, 4, 6}

= {1, 3, 5}

Now A (C B) = {4, 6, 7, 8, 9} {1, 3, 5}

= {4, 6, 7, 8, 9}