Question 916124: Determine whether the function f : Z × Z → Z is onto if
a) f (m, n) = m.
b) f (m, n) = |n|.
c) f (m, n) = m − n.
I know that "is f onto" is equivalent to "Given any integer k, can you find two integers m and n such that [insert function value here] = k?"
Wouldn't that make ALL of them onto? If not, why not?
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! No. Not (b) since absolute values are never negative!
Let's go through them:
(a) is onto because for any k ∈ Z, f(k,n) = k, for any n ∈ Z
(b) is not onto because for any k ∈ Z where k < 0,
f(m,n) = |n| ≠ k for all m,n ∈ Z
(c) is onto because for any k ∈ Z, f(k+1,1) = (k+1)-1 = k
Edwin
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