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

set containing the first n natural numbers. Then {0, ..n} R is the set of all sequences of real numbers with a length of n. As an abbreviation, well

1

n tot n write R for {0,..n} R. We can use R as the type of real arrays of

length n. Of course, if a Rn and i {0, ..n}, then a(i) is item i of array a. The expression a(i) is not defined if a Rn but i / {0, ..n}.

Let

= {a 7 Rn,b 7 B,i 7 N} Write specifications on for the problems below. The following

function may be helpful count R RN

n tot 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. I.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.