If n(A) = 65, n(B) = 32 and n(A ∩ B) = 14, then n(A B) equals: - Vidyadip

MCQ

If $\ce{n(A) = 65, n(B)} = 32$ and $\ce{n(A ∩ B)} = 14,$ then $\ce{n(A \triangle B)}$ equals:

A
$65$
B
$47$
C
$97$
✓
$69$

✓

Answer

Correct option: D.

$69$

$ \text{n}(\text{A}\triangle\text{B})= \text{n(A - B)} +\text{ n(B - A)}$
$\therefore(\text{A}\triangle\text{B})=\text{ (A - B)} ∪ \text{(B - A)}$
$\Rightarrow (\text{A}\triangle\text{B}) = \text{n(A)} \text{ -n(A ∩ B)} +\text{ n(B)} − \text{n(A ∩ B)}$
$\Rightarrow (\text{A}\triangle\text{B})=\text{ n(A)} +\text{ n(B)} \text{ -2n} (A∩B)$
$= 65 + 32 - 2 \times 14$
$= 69$

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