Question

Match the following:

Given U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are the cardinal numbers of U, A and B respectively.

Number of:

• A. A - iii, B - iv, C - ii, D- i
• B. A - iii, B - iv, C - i, D- ii
• C. A - ii, B - iv, C - iii, D- i
• D. A - i, B - iv, C - ii, D- iii

Answer 1

The correct option is A

A - iii, B - iv, C - ii, D- i

1) Neither in A nor in B

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

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

We know that

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

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

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 $(A\cap B)$

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

4) Elements either in A or in B = Elements in $(A\cup B)=n(A\cup B)$