Question

Let f be the subset of Z x Z defined by f = {(ab, a+b): a, b ∈ Z}. Is f a function from Z to Z? Justify your answer.

Answer 1

The relation f is defined as f = {(ab, a+ b): a, b ∈ 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.
Since 2, 6, -2, -6 ∈ Z
(2 x 6, 2 + 6), (-2 x -6, -2 + (-6)) ∈ f
i.e., (12, 8), (12, -8) ∈ f
It can be seen that the same first element i.e.,12 corresponds to two different images i.e., 8 and -8. Thus, relation f is not a function.