Question

Let $f:N\times N\to N-\left\{1\right\}$ be defined as $f(m,n)=m+n$, then function $f$ is ______.

• A. One-One and onto
• B. Many- One and not onto
• C. One- One and not onto
• D. Many- One and onto

Answer 1

Answer: (A)

One-One and onto

Given $f(m,n)=m+n$

Range of this function is set of all natural numbers except $1$

[since least value of $m$ and $n$ is $1$]

Therefore the range and co-domain are equal

Therefore it is onto

For every $(m,n)$, there exists only one $m+n$

Therefore it is one-one also

Hence, $f$ is one-one and onto.