The answers to exercise marked [BB] can be found in the Back of the Book.
Determine whether each of the following defines a one-to-one and/or an onto function, Either give a proof or exhibit a counterexample to justify every answer.
(a) [BB] f(n, m)= 2n +3m; ƒ: N × N → N
(b) [BB] f(n, m)= 2n +3m, ƒ: Z × Z → Z
(c) ƒ{n, m) = 14n +22m; ƒ: N×N→N
(d) ƒ(n, m) = 89n + 246m; ƒ: Z × Z → Z
[Hint: 1 = (−17) (246) +47(89)]
(e) f(n,m)= n2+m2+1; f: Z×Z→N
(f) f(n,m)= +1; f: N×N→N
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