Question

1.
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 (1) A' (ii) B' (iii) (AUC) (iv) (AUB)' (v) (A')'
(vi) (B-C)​

Answer 1

${\huge{\underbrace{\rm{Answer}}}}$

★ Given :

• 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 :

1. A'
2. B'
3. A$\cup$C
4. (A$\cup$B)'
5. (A')'
6. (B-C)

★ Solution :

1. A' or A compliment

In this , we will consider all the elements other than those present in set A.

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

2. B' or B compliment

In this , we will consider all the elements other that those present in set B .

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

3. $\rm\bold{A \cup C}$

or A union C

In this , we will take all the elements present in set A and set C (avoiding repetition).

$\rm{A \cup C }$ = { 1 , 2 , 3 , 4 , 5 , 6 }

4. $\rm\bold{(A \cup B)'}$

In this , we will first take union of set A and set B ..

(A$\cup$B) = { 1 , 2 , 3 , 4 , 6 , 8 }

Now , we will take it compliment , means all other elements except the ones present in the union .

(A$\cup$B)' = { 5 , 7 , 9 }

5. (A')'

The compliment of a compliment is the same set .

(A')' = A = { 1 , 2 , 3 , 4 }

6. ( B - C )

In this , we will remove all the elements from set B which belongs to set C .

( B - C ) = { 2 , 8 }