Suppose n > 0 is a fixed member of N. Remember that {0,..n} is the set...

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Suppose n > 0 is a fixed member of N. Remember that {0,..n} is the set containing the first n natural numbers. Then {0, ..n} tot R is the set of all sequences of real numbers with a length of n. As an abbreviation, we'll 1 write R for {0,..n} R. We can use R" as the type of real arrays of length n. Of course, if a R" and i {0,..n}, then a(i) is item i of array a. The expression a(i) is not defined if a R" but i & {0, ..n}. Let ={"a"R", b B, i N} Write specifications on for the problems below. The following function may be helpful count Rn x R tot N count(a, x) = {j= {0,..n} | a(j) = x}| (a) [5] Reverse: The final value of a should be the reverse of its initial value. (b) [5] Sorted: The final value of a is a nondecreasing sequence of values. 1.e. each item should be greater or equal to all earlier items. (c) [5] Permutation: The final value of a contains the same items as its initial value, in the same quantities, though perhaps not in the same order. Suppose n > 0 is a fixed member of N. Remember that {0,..n} is the set containing the first n natural numbers. Then {0, ..n} tot R is the set of all sequences of real numbers with a length of n. As an abbreviation, we'll 1 write R for {0,..n} R. We can use R" as the type of real arrays of length n. Of course, if a R" and i {0,..n}, then a(i) is item i of array a. The expression a(i) is not defined if a R" but i & {0, ..n}. Let ={"a"R", b B, i N} Write specifications on for the problems below. The following function may be helpful count Rn x R tot N count(a, x) = {j= {0,..n} | a(j) = x}| (a) [5] Reverse: The final value of a should be the reverse of its initial value. (b) [5] Sorted: The final value of a is a nondecreasing sequence of values. 1.e. each item should be greater or equal to all earlier items. (c) [5] Permutation: The final value of a contains the same items as its initial value, in the same quantities, though perhaps not in the same order.