Let G be the group of all nonzero real numbers under the operation ∗ which is the ordinary multiplication of real numbers, and let H be the group of all real numbers under the operation \#, which is the addition of real numbers.
(a) Show that there is a mapping F : G→H of G onto H which satisfies F(a∗b) = F(a) # F(b) for all a, b ∈ G [i.e., F(ab)=F(a)+F(b)].
(b) Show that no such mapping F can be 1-1.
