Question

If $Q=\left\{x:x=\frac{1}{y},\mathrm{where}y\in N\right\}$, then

• A. $0\in Q$
• B. $1\in Q$
• C. $2\in Q$
• D. $\frac{2}{3}\in Q$

Answer 1

The correct option is B

$1\in Q$

Explanation for the correct option.

Option B: $1\in Q$

Given that, $Q=\left\{x:x=1/y,\mathrm{where}y\in N\right\}$

$1\in Q$ implies $$\begin{gathered} \frac{1}{y}=1 \\ \Rightarrow y=1 \end{gathered}$$

Hence option B is correct.

Explanation for incorrect options.

Option A: $0\in Q$

If $0\in Q$ then this implies $\frac{1}{y}=0$ which is not possible as $y\in N$.

Hence, option A is incorrect.

Option C: $2\in Q$

If $2\in Q$ then this implies:

$$\begin{gathered} \frac{1}{y}=2 \\ y=\frac{1}{2}\notin N \end{gathered}$$

Hence, option C is incorrect.

Option D: $\frac{2}{3}\in Q$

If $\frac{2}{3}\in Q$ then this implies

$$\begin{gathered} \frac{1}{y}=\frac{2}{3} \\ y=\frac{3}{2}\notin N \end{gathered}$$

Hence, option D is incorrect.

Therefore, option B is correct.