2. Let A = {1,2,3,4}. Let F be the set of all functions from A to...

2. Let A = {1,2,3,4}. Let F be the set of all functions from A to A. Recall that IA ∈ F is the identity function on A given by IA(x) = x for all x ∈ A. Consider the function E : F → A given by E(f) = f(1) for all f ∈ F.
(a) Is the function E one-to-one? Prove your answer.

(b) Is the function E onto? Prove your answer.

(c) How many functions f ∈ F are there so that E(f) = E(IA)? Explain.

(d) How many onto functions f ∈ F are there so that E(f) = E(IA)? Explain.

Expert Solution

hi if you have any doubts please c

Colby Messinger answered 1 year ago

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