Please show the work This extra credit assignment comprising three problems asks you to explore and ultimately produce and prove an example of this

Please show the work

 In this assignment, A, B and C represent sets, g is a function from A to B, and f is a function from B to C, and h stands for f composed with g, which goes from A to C.

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7.  Inspired by your finding in 6, find three sets A,B,C, not necessarily different from each other, and two functions f and g so that g is a function from A to B, f is a function from B to C, and h is bijective, while neither f nor g is bijective. Prove that your example is correct.

8. Give a brief, intuitive explanation of how the specific ways in which your f and g fail to be bijective cancel each other out in a sense and make it possible for h to be bijective.