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 co-domain is $N$
• D. None of the above

Answer 1

Answer: (A)

$R =\{(1,2),(2,4),(3,6),(4,8), \ldots . .\}$
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 co-domain is also $N$, and the range is the set of even natural numbers.