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Question: 6 4 pts let x and y be finite sets...

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(6) (4 pts) Let X and Y be finite sets, and denote the set of maps f : X → Y by Y. Show that Fx = Y x Compare with your results to problem 5 (that is, observe that this formula gives the results in problem 5) Hint. Let X - [r..,xm] and Y -v yn]. Now let f:X -Y be any map. How many possible values can f(ri) take on? How many possible values can f(r2) take on? Therefore, how many pairs (f(x),f(q)) are possible? (Caution: a pair (Uny) is not the same as the set {w,y1. For example, the pairs (vi, y2) and (y2. yi) are distinct, but the sets [v.y2) and [y2,i] are the same.) Now generalize the case when m- 2 to a general m

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