Answer to Question #281685 in Discrete Mathematics for jade

Question #281685

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


1
Expert's answer
2021-12-21T18:27:05-0500

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

is a surjective function or onto function because for (zZ)\forall(z\in Z) the pair (z,1)dom(f)=Z×Z(z,1)\in dom(f)=Z \times Z and f(z,1)=z1=zf(z,1)=z\cdot 1=z . So im(f)=Z.


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