Textbook Problem

De?ne $F:{\text{Z}}^{+}\times {\text{Z}}^{+}\to {\text{Z}}^{+}$ and $G:{\text{Z}}^{+}\times {\text{Z}}^{+}\to {\text{Z}}^{+}$ as follows: For each $\left(n,m\right)\in {\text{Z}}^{+}\times {\text{Z}}^{+}$ , $F\left(n,m\right)=3^n{5}^m$ and $G\left(n,m\right)=3^n{5}^m$ .

a. Is F one-to-one? Prove or give a counterexample.
b. 1s G one-to-one? Prove or give a counterexample.