SOLUTION: Determine whether the function f : Z × Z &#8594; Z is onto if a) f (m, n) = m. b) f (m, n) = |n|. c) f (m, n) = m &#8722; n. <br> I know that "is f onto" is equivalent to "Giv

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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(20056)   (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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