Let U = {1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i) It is given that

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 2, 3, 4}

B = {2, 4, 6, 8}

C = {3, 4, 5, 6}

To find, A'

The complement of set A is the set of all elements of U which are not the elements of A.

A' = U−A

{1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4}

= {5, 6, 7, 8, 9}

A’ = {5, 6, 7, 8, 9}

(ii) To find, B'

The complement of set A is the set of all elements of U which are not the elements of A.

B' = U−B

{1, 2, 3, 4, 5, 6, 7, 8, 9} -  {2, 4, 6, 8}

= {1, 3, 5, 7, 9}

B’ = {1, 3, 5, 7, 9}

(iii) To find, (A U C)'

The complement of set A is the set of all elements of U which are not the elements of A.

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

(A U C)' = U − (A U C)

{1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 5, 6}

=  {7, 8, 9}

(A U C)’ = {7, 8, 9}

(iv) To find, (A U B)’

{1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 5, 6, 7, 8}

The complement of set A is the set of all elements of U which are not the elements of A.

=  {5, 7, 9}

(A U B)’ = {5, 7, 9}

(v) To find, (A')'

The complement of set A is the set of all elements of U which are not the elements of A.

(A')' = A

= {1, 2, 3, 4}

(A’)’ = {1, 2, 3, 4}

(vi) To find, (B− C)'

The complement of set A is the set of all elements of U which are not the elements of A.

B − C = {2,8}

(B− C)' = U − (B− C)

{1, 2, 3; 4, 5, 6, 7, 8, 9} - {2,8}

= {1, 3, 4, 5, 6, 7, 9}

So we get

(B – C)’ = {1, 3, 4, 5, 6, 7, 9}