Question

Match the following:

Given U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are no. of elements in U, A, B respectively.

Number of:

(1) Elements neither in A nor in B (A) $n(A\cup B)$

(2) Elements only in A (B)$n\left(B\right)-n(A\cap B)$

(3) Elements only in B (C)$n\left(A\right)-n(A\cup B)$

(4) Elements either in A (or) in B (D)$n\left(U\right)-n(A\cup B)$

(E)$n\left(A\right)-n(A\cap B)$

• A. 1-D, 2- E, 3- B, 4- A
• B. 1-D, 2- B, 3- E, 4- A
• C. 1-D,2- C,3- B,4- A
• D. 1-D,2- C,3- A,4-B

Answer 1

The correct option is A

1-D, 2- E, 3- B, 4- A

1) Neither in A nor in B

$\Rightarrow \text{not in A and not in B}$
$\Rightarrow A^I\cap B^I$
$n(A^I\cap B^I)=n(A\cup B{)}^I$
$=n(\cup )-n(A\cup B)\Rightarrow D$

2) From Venn diagram, elements only in A is represented as,

We know that

Elements in A = Elements in (A - B) $\cup$ elements in $(A\cup B)$

$n\left(A\right)=n(A-B)+n(A\cap B)$
$So,n(A-B)=n\left(A\right)-n(A\cap B)\Rightarrow \left(E\right)$

3) Elements only in B is represented using Venn diagram as,

We can see that

Elements in B = Elements in (B - A) $\cup$ Elements in $(A\cap B)$

$n\left(B\right)=n(B-A)+n(A\cap B)$
$n(B-A)=n\left(B\right)-n(A\cap B)\to \left(B\right)$

4) Elements either in A or in B