Question

If $A=\{x:x$ is a multiple of $2\},B=\{x:x$ is a multiple of $5\}$ and $C=\{x:x$ is a multiple of 10$\}$, then $A\cap (B\cap C)$ is equal to

• A. $A$
• B. $B$
• C. $C$
• D. $\{x:x$ is a multiple of $100\}$

Answer 1

Answer: (C)

$C$

$A=\{x:x$ is a multiple of $2\}=\{2,4,6,8,10,12,14,....\}$

$B=\{x:x$ is a multiple of $5\}=\{5,10,15,20,25,....\}$ and

$C=\{x:x$ is a multiple of $10\}=\{10,20,30,40,....\}$

Here, $C\subset A$ and $C\subset B$
$C=A\cap B=A\cap (B\cap C)$

$=A\cap C=C$