Let S = {s | s : {1,2,3} {1, 2, 3}}. Notice that each element...

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Let S = {s | s : {1,2,3} → {1, 2, 3}}. Notice that each element of S is a sequence and so it makes sense to ask whether an element in S is increasing, decreasing, etc. (Part of this question is interpreting what is written.) 1. Find S. 2. How many elements in S are increasing? 3. How many elements in S are decreasing? 4. How many elements in S are non-increasing or (inclusively) non-decreasing? Show all your work and explain your answers. Let S = {s | s : {1,2,3} → {1, 2, 3}}. Notice that each element of S is a sequence and so it makes sense to ask whether an element in S is increasing, decreasing, etc. (Part of this question is interpreting what is written.) 1. Find S. 2. How many elements in S are increasing? 3. How many elements in S are decreasing? 4. How many elements in S are non-increasing or (inclusively) non-decreasing? Show all your work and explain your answers.