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Question: course cryptography question 6 please i included question 5 because...

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Course: Cryptography

Question 6 please (I included question 5 because part of question 6 asks about Q5)

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(5) (2 pts) Let X be a set with 2 elements and let Y be a set with three elements. How many maps are there from X to Y? How many maps are there from Y to X? (6) (4 pts) Let X and Y be finite sets, and denote the set of maps f : X → Y by Yx. Show that YXI Y Compare with your results to problem 5 (that is, observe that this formula gives the results in problem 5). Hint. Let X = {xi, ,z,n} and Y = {yi, ,Yn). Now let f : X → Y be any map. How many possible values can f() take on? How many possible values can f(r2) take on? Therefore, how many pairs (f(x),f(x2)) are possible? (Caution: a pair (yi,y) is not the same as the set {Unyh For example, the pairs (yi,Y2) and (n,y) are distinct, but the sets {y,y1 and {y2,nl are the same.) Now generalize the case when m-2 to a general m

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