If $$n(A$$−$$B)=14$$,$$n(A$$∪$$B)=29$$ and $$n(A$$∩$$B)=9$$ , then $$n(B$$−$$A)$$ is

$$n(A$$∪$$B)=n(A$$−$$B)+n(B$$−$$A)+n(A$$∩$$B)$$∴$$29=14+n(B$$−$$A)+9$$∴$$n(B$$−$$A)=6$$

Operations on Sets

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Question

$If n (A - B) = 14, n (A \cup B) = 29 and n (A \cap B) = 9, then n (B - A) is$

Moderate

Solution

$\begin{array}{l} n (A \cup B) = n (A - B) + n (B - A) + n (A \cap B) \\ ∴ 29 = 14 + n (B - A) + 9 \\ ∴ n (B - A) = 6 \end{array}$

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