A relation R is defined from N to N as $R= \{(ab, a+b): a,b∈ N\}$. Is R a function from N to N? Justify your answer.

R is not a function

The relation f is defined as $f= \{(ab, a + b): a, b = Z\}$

We know that a relation ƒ from a set A to a set B is said to be a function if every element of set A has unique images in set B.

Let ab = 16. We have following possibilities.

If a = 1, b = 16, then a + b = 17

If a = 2, b = 8, then a + b = 10

If a = 4, b = 4, then a + b = 8

Thus, first element '16' has three corresponding second elements 17, 10, 8.

So, Relation R is not a function.