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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.

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