Question

Determine whether the function f : z × z → z is onto if

a.f(m,n)=m+n. b)f(m,n)=m2+n2.
c.f(m,n)=m.
d.f(m,n) = |n|.
e.f(m,n)=m−n.

Answer 1

a. Yes;
`\mathbb Z` is closed under addition
b. No;
`m^2+n^2\ge0` for any integers
`m,n`
c. Yes; self-evident
d. No; similar to (b), because
`|n|\ge0` for any
`n\in\mathbb Z`
e. Yes;
`\mathbb Z` is closed under subtraction