Question

If $A:\{x:x\text{is a multiple of}3\}$ and $B=\{x:x\text{is a multiple of}4\}$ and $C=\{x:x\text{is a multiple of}12\}$, then which one of the following is a null set?

• A. $\left(A/B\right)\cup C$
• B. $\left(A/B\right)/C$
• C. $(A\cap B)\cap C$
• D. $(A\cap B)/C$

Answer 1

Answer: (D)

$(A\cap B)/C$

$A:\{x:x\text{is a multiple of}3\}$

$A=\{3,6,9,12,15,18,21,....\}$

$B=\{x:x\text{is a multiple of}4\}$

$B=\{4,8,12,16,20,24,......\}$

$C=\{x:x\text{is a multiple of}12\}$

$C=\{12,24,36,48,60,......\}$

Then, $A\cap B=\{12,24,36,48,60,.....\}$

$⟹(A\cap B)/C$ is a null set.