# If $S_1=\{1,2,...................20\}$, $S_2=\{a,b,c,d,e\}$, $S_3=\{a,c,e,f\}$, then no. of elements of $(S_1\times S_2)\cap (S_1\times S_3)$ is ?

$\begin{array}{1 1} 40 \\ 60 \\ 80 \\ 100 \end{array}$

Toolbox:
• $(A\times B)\cap (A\times C)=A\times (B\cap C)$
• $n(A\times B)=n(A).n(B)$
$n(S_1)=20,\:\:n(S_2)=5\:\:n(S_3)=4,\:\:n(S_2\cap S_3)=3$
$n\big((S_1\times S_2)\cap (S_1\times S_3)\big)=$
$n\big(S_1\times (S_2\cap S_3)\big)=$
$n(S_1).n(S_2\cap S_3)=20\times 3=60$
answered May 18, 2013
edited May 18, 2014