Question

If Q = \\{ x:x = \dfrac{1}{y} , where y \in N\\} , then
A) $0 \in Q$
B) $1 \in Q$
C) $2 \in Q$
D) $\dfrac{2}{3} \in Q$

Answer 1

They have asked to check which number from the option is the right corresponding given condition. In order to find the correct answer you have to have knowledge about what is a natural number (N) and rational number (Q). After that, put every option value in a given condition to find which number satisfies the given condition.

Complete step by step answer:
The given condition is,
$\Rightarrow Q = \\{ x:x = \dfrac{1}{y}\\}$
So, to find the solution for a given one you have to check all options values and put it in the given condition so you will get to know the correct one.
So, let’s put first option,
First option value is $1$ so put it in $x = \dfrac{1}{y}$
After putting we will get,
$\Rightarrow x = \dfrac{1}{0}$
Since, it is given that $y \in N$ but $0$ does not belong to N. so, option $1$ is not correct.
Now, second option value is $1$ so put it in $x = \dfrac{1}{y}$
After putting we will get,
$\Rightarrow x = \dfrac{1}{1}$
Since, they also given that $y \in N$ and also $1$ belongs to N. so, option $2$ is correct.
Third option value is $2$ so put it in $x = \dfrac{1}{y}$
After putting we will get,
$\Rightarrow x = \dfrac{1}{2}$
Since, they also gave that $y \in N$ but $\dfrac{1}{2}$ does not belong to N. so, option $3$ is not correct.
Fourth option value is $\dfrac{2}{3}$ so put it in $x = \dfrac{1}{y}$
After putting we will get,
$\Rightarrow x = \dfrac{3}{2}$
Since, they also gave that $y \in N$ but $\dfrac{3}{2}$ does not belong to N. So, option $4$ is not correct.
Hence, option (B) $1 \in Q$ is correct.

Note:
In this question we have discussed natural numbers and rational numbers. Natural numbers can be considered the basis of most if not all common number sets. For example, the integers are simply the natural numbers ℕ, 0, and the negatives of the natural numbers. Rational numbers can be defined as the quotients of integers, that is, fractions.