In a class of 30 students, 10 take Mathematics, 15 take Physics, and 10 take neither. The number of students who take both mathematics and physics is -

Total number of students $n (μ) = 30$

$n (M) = 10$

$n (P) = 15$

$n (M \cup P) = 30 - 10 = 20$

Let $n (M \cap P) = x$

$n (M \cup P) = n (M) + n (P) - n (M \cap P)$

$20 = 10 + 15 - x$

$x = 5$

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