Question

Let $N$ be the set of natural numbers and the relation $R$ be defined such that $\{R=(x, y): y$ $=2 x, x, y \in N\}$. Then,

• A. $R$ is a function
• B. $R$ is not a function
• C. domain range and codomain is $N$
• D. None of the above

Answer 1

Answer: (A)

$R=\{(1,2),(2,4),(3,6),(4,8) \ldots \ldots\}$
Since, every natural number $N$ has one and only one image, this relation $R$ is a function.
The domain of $R$ is the set of natural number i.e., $N$. The codomain is also $N$, and the range is the set of even natural numbers.