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

Explanation

The relation `f` is defined as ` f={(ab, a+b):a,b in Z}`
We know that a relation `f` 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=2, 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.