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I am having the most trouble with 1d: 1. a. Prove that if f : A...

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Advance Math

I am having the most trouble with 1d:

1. a. Prove that if f : A ? B, g : B ? C, and g ?f : A ? C is a1-to-1 surjection, then f is 1-to-1 and g is a surjection.
Proof.
b. Prove that if f : A ? B, g : B ? C, g ? f : A ? C is a 1-to-1surjection, and g is 1-to-1, then f is a surjection.
Proof.
c. Prove that if f : A ? B, g : B ? C, g ? f : A ? C is a 1-to-1surjection, and f is a surjection, then g is 1-to-1.
Proof.
d. Find functions f : R ? R and g : R ? R such that g?f is a 1-to-1surjection , f is not a surjection, and g is not 1-to-1.

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