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

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 a 1-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-1 surjection, 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-1 surjection, 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-1 surjection , f is not a surjection, and g is not 1-to-1.

Expert Solution

Colby Messinger answered 10 months ago

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