Question:
If n(A ∩ B′) = 9, n(A' ∩ B) = 10 and n(A ∪ B) = 24, then n(A × B) = ___________ .
Solution:
$\left.\begin{array}{rl}n\left(A \cap B^{\prime}\right) & =9 \\ \text { If } n\left(A^{\prime} \cap B\right) & =10 \\ n(A \cup B) & =24\end{array}\right\}$ given
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n(A) = n(A ⋃ B) − n(A' ∩ B)
n(B) = n(A ⋃ B) − n(A ∩ B')
i.e n(A) = 24 − 10 =14
$n(B)=24-9=15$
$\therefore n(A \times B)=n(A) \cdot n(B)$
n(A × B) = 14 × 15 = 210