Let \(S=\{x:x \text{ is a positive multiple of }3 \text{ less than }100\}\),
\[ P=\{x:x \text{ is a prime less than }20\} \]
Then, \(n(S)+n(P)\) is
(a) 34
(b) 31
(c) 33
(d) 30
Solution
Positive multiples of \(3\) less than \(100\):
\[ 3,6,9,\ldots,99 \]
Number of elements in \(S\):
\[ \frac{99}{3}=33 \]
Therefore,
\[ n(S)=33 \]
Prime numbers less than \(20\):
\[ 2,3,5,7,11,13,17,19 \]
Thus,
\[ n(P)=8 \]
Hence,
\[ n(S)+n(P)=33+8 \]
\[ =41 \]
Answer
\[ \boxed{41} \]
Hence, none of the given options is correct.