Describe surjective and injective properties of functions

Question

Problem:

Question- Proofs involving surjective and injective properties of general functions:

Let f : A \rightarrow B and g : B \rightarrow C be functions, and let h = g\circf be the composition of g and f.

For each of the following statements, either give a formal proof or provide a counterexample. (A counterexample means a specific example of sets A, B, C and functions f : A \rightarrow B, and g : B \rightarrow C, for which the statement is false.)

Part 1- If f and g are injective, then h is injective.

Part 2- If f and g are surjective, then h is surjective.

Part 3- If h is injective, then f is injective.

Part 4- If h is injective, then g is injective.

Part 5- If h is surjective, then f is surjective.

Part 6- If h is surjective, then g is surjective

Please show all the calculations step by step.