Operations on Sets

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Question

$If S = {x ∣ x is a positive multiple of 3 and less than 100} and P = {x ∣ x is a prime number less than 20} . Then n (S) + n (P)$

Moderate

Solution

$S = {x ∣ x is a positive multiple of 3 and less than 100}$
$\begin{aligned} = {3, 6, 9, \dots, 99} \\ ∴ n (S) = 33 \end{aligned}$
$\begin{aligned} and P = {x ∣ x is a prime number less than 20} \\ = {2, 3, 5, 7, 11, 13, 17, 19} \end{aligned}$
$\begin{array}{l} ∴ n (P) = 8 \\ n (S) + n (P) = 33 + 8 = 41 \end{array}$

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