Let S = {x : x is a positive multiple of 3 less than 100}, P = {x : x is a prime number less than 20}, Then, n(S) + n(P) = _____
Solution
\[ S = \{3,6,9,\ldots,99\} \]
Number of multiples of 3 less than 100:
\[ \frac{99}{3} = 33 \]
Therefore,
\[ n(S)=33 \]
Prime numbers less than 20 are
\[ \{2,3,5,7,11,13,17,19\} \]
\[ n(P)=8 \]
Hence,
\[ n(S)+n(P)=33+8=41 \]
Answer
\[ \boxed{41} \]