1. What three things must we check to determine whether a function S -> S' is an isomorphism of a binary structure (S, *) with (S, *)?
In Exercises 2 through 4, determine whether the given map is an isomorphism of the first binary structure with the second. (See Exercise 1.) If it is not an isomorphism, why not?
2. (Z, +) with (Z, +) where f(n) = 2n for n ∈ Z
3. (Q+) with (Q+) where f(x) = x/2 for x ∈ Q
4. (R, *) with (R, *) where f(x) = x for x ∈ R.