(Solved): Consider two functions \( f: S \rightarrow T \) and \( h: T \rightarrow U \) ...

???????

Consider two functions \( f: S \rightarrow T \) and \( h: T \rightarrow U \) for non-empty sets \( S, T, U \). Decide whether each of the following statements is true or false, and prove each claim. a) If \( \boldsymbol{h} \circ \boldsymbol{f} \) is injective, then \( \boldsymbol{h} \) is injective. b) If \( \boldsymbol{h} \circ \boldsymbol{f} \) is injective, then \( \boldsymbol{f} \) is injective. c) If \( \boldsymbol{h} \circ \boldsymbol{f} \) is injective and \( \boldsymbol{f} \) is surjective, then \( \boldsymbol{h} \) is injective.