Question

Determine whether f : Z × Z → Z is onto if f(m,n)= m-n

Answer 1

The mapping f : Z × Z → Z , where f(m,n)= m-n

is a surjective function or onto function because for $\forall(z\in Z)$ the pair $(z,1)\in dom(f)=Z \times Z$ and $f(z,1)=z\cdot 1=z$ . So im(f)=Z.