Determine whether f : Z × Z → Z is onto if f(m,n)= m-n
The mapping f : Z × Z → Z , where f(m,n)= m-n
is a surjective function or onto function because for ∀(z∈Z)\forall(z\in Z)∀(z∈Z) the pair (z,1)∈dom(f)=Z×Z(z,1)\in dom(f)=Z \times Z(z,1)∈dom(f)=Z×Z and f(z,1)=z⋅1=zf(z,1)=z\cdot 1=zf(z,1)=z⋅1=z . So im(f)=Z.
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