Question

If n(A ∩ B′) = 9, n(A' ∩ B) = 10 and n(A ∪ B) = 24, then n(A × B) = ___________ .

Answer 1

$\mathrm{If}\left.\begin{array}{l}n(A\cap B\text{'})=9\\ n(A\text{'}\cap B)=10\\ n(A\cup B)=24\end{array}\right\}\mathrm{given}$



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 × B) = n(A) . n(B)
n(A × B) = 14 × 15 = 210