Let R = {x : x ∈ N, x is multiple of 3 and x ≤ 100} and S = {x : x ∈ N, x is multiple of 5 and x < 100}. What is the number of elements in (R ∩ S) × (S ∩ R)?

Solution: $R=\{x:x\in N,\ x\text{ is multiple of }3,\ x\le 100\}$ $S=\{x:x\in N,\ x\text{ is multiple of }5,\ x<100\}$ $R\cap S$ contains numbers which are multiples of both $3$ and $5$. So, $R\cap S$ contains multiples of $15$. Multiples of $15$ less than $100$ are: $15,30,45,60,75,90$ So, $|R\cap S|=6$ Also, $S\cap R=R\cap S$ Therefore, $|(R\cap S)\times(S\cap R)|=6\times6=36$ So, the correct answer is $36$.