Define F: Z+ Z+ Z+ and G: Z+ Z+ Z+ as follows: For all (n, m) Z+ Z+, F(n, m) = 3n 5m and
Chapter 7, Problem 31(choose chapter or problem)
Define F: \(\mathbf{Z}^{+} \times \mathbf{Z}^{+} \rightarrow \mathbf{Z}^{+}\) and \(G: \mathbf{Z}^{+} \times \mathbf{Z}^{+} \rightarrow \mathbf{Z}^{+}\) as follows: For all \((n, m) \in \mathbf{Z}^{+} \times \mathbf{Z}^{+}\),
\(F(n, m)=3^{n} 5^{m}\) and \(G(n, m)=3^{n} 6^{m}\).
a. Is F one-to-one? Prove or give a counterexample.
b. Is G one-to-one? Prove or give a counterexample.
Text Transcription:
mathbf Z^+ times mathbf Z^+ rightarrow mathbf Z^+
G: mathbf Z^+ times mathbf Z^+ rightarrow mathbf Z^+
(n, m) in mathbf Z^+ times mathbf Z^+
F(n, m)=3^n 5^m
G(n, m)=3^n 6^m
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