**Puzzle 17**. We must show that if \\(S \subseteq T\\) then \\(f(S) \subseteq f(T)\\), which is equivalent to saying that \\(s \in f_\ast(S) \rightarrow s \in f_*(T)\\). But if \\(s \in f_\ast(S)\\) then \\(s = f(x)\\) for some \\(x \in S\\), which means \\(x \in T\\), so \\(s \in f_\ast(T)\\), as was to be shown.