Question

Let $S=\left\{x|x\text{is a positive multiple of 3 less than 100}\right\},$
$P=\left\{x|x\text{is a prime number less than 20}\right\}.$
Then $n\left(s\right)+n\left(p\right)$ is

• A. $41$
• B. $34$
• C. $30$
• D. $33$

Answer 1

The correct option is A $41$

Given : $S=\left\{x|x\text{is a positive multiple of 3 less than 100}\right\}$

$P=\left\{x|x\text{is a prime number less than 20}\right\}$

$\therefore S=\{3,6,9,12,...,99\}$

$\Rightarrow n\left(S\right)=33...\left(1\right)$

And $P=\{2,3,5,7,11,13,17,19\}$

$\Rightarrow n\left(P\right)=8...\left(2\right)$

$\Rightarrow n\left(S\right)+n\left(P\right)=33+8=41.$

Hence, the correct option is (B).