Let a E A and f: A→A be a function such that a ran (f). Suppose that h: w → A satisfies (a) h (0) = a (b) h (n+) = f (h (n)), for all n €w. Assume that h is one-to-one and onto A. Prove that f is one-to-one.

Q: Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well %3D defined.

A: we need to prove homomorphism

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A: Solution :-

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A: Probability of at least one accident = p(t) Probability of no accident = 1 - p(t)

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A: To Show: Show that for any function f : X → Y, there are two functions g: S → T and h: X → S such…

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Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

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A: We shall use the intermediate value theorem to answer this question

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A: We use definition of function .

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