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

Assuming "z" is $\mathbb Z$, the set of integers:

a. yes
b. no; $m^2+n^2$ will always be a non-negative integer
c. yes
d. no; same reason as (b)
e. yes