Question

Consider the following domain and range for the relation from set $X$ to set $Y$ such that $x-y=2n;\text{where}n\text{is a integer}$.
$X:\{4,5,6,7\}Y:\{2,6,7,9\}x\in X\&y\in Y$
Is this a function?

• A. Yes. It is a function as the number of elements of domain equals the number of elements in $y.$
• B. No. It is not a function.

Answer 1

The correct option is B No. It is not a function.

Relation $x-y=2n;\text{where}n\text{is a integer}$

Let's generate the mapping diagram.

Here, we find that $4$ from set $X$ is mapped to two elements of set $Y$.
similiarly, other elements of set $X$ are also mapped with more than 2 elements of set $Y$.

$\therefore$ This is not a function.