Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let...

Unless otherwise noted, all sets in this module are finite. Prove the following statements...

1. Let S = {0, 1, . . . , 23} and define f : Z→S by f(k) = r when 24|(k−r). If g : S→S is defined by (a) g(m) = f(7m) then g is injective and (b) g(m) = f(15m) then g is not injective.

2. Let f : A→B and g : B→C be injective. Then g ◦f : A→C is injective.

3. Let f : A→B and g : B→C be surjective. Then g ◦ f : A→C is surjective.

4. There is a surjection f : A→B such that f −1 : B→A is not a function.

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Expert Solution

Colby Messinger answered 1 year ago

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