Question

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

Answer 1

We observe that $1\times 4=4$ and $2\times 2=4$

$\Rightarrow (1\times 4,1+4)ϵf$ and $(2\times 2,2+2)ϵf$

$\Rightarrow (4,5)ϵf$ and $(4,4)ϵf$

which shows that f is not a function from Z to Z.