Question

If $A=\{1,2\},$ $B=\{2,4\}$ and $C=\{4,6\},$ then $A\cap (B\cap C)$ = ___.

• A. $\left\{\right\}$
• B. $\{1,2,4,6\}$
• C. $(A\cup B)\cup C$
• D. $(A\cap B)\cap C$

Answer 1

Answer: (A), (D)

The correct options are
A $\left\{\right\}$
D $(A\cap B)\cap C$

Given $A=\{1,2\},$ $B=\{2,4\}$ and $C=\{4,6\}.$
$A\cap (B\cap C)=\{1,2\}\cap \left(\right\{2,4\}\cap \{4,6\left\}\right)=\{1,2\}\cap \left\{4\right\}=\left\{\right\}$
Also, $(A\cap B)\cap C=\left(\right\{1,2\}\cap \{2,4\left\}\right)\cap \{4,6\}=\left\{2\right\}\cap \{4,6\}=\left\{\right\}.$

Note that $(A\cap B)\cap C=A\cap (B\cap C)$ is known as the associative property of intersection of sets.