Solution: Exercises 6–9 each contain a while loop annotated

Chapter 5, Problem 9E

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Problem 9E

Exercises 6–9 each contain a while loop annotated with a preand a post-condition and also a loop invariant. In each case, use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions.

[Pre-condition: a = A and A is a positive integer.]

while ( a > 0)

1. a := a − 2

end while

[Post-condition: a = 0 if A is even and a = −1 if A is odd.] loop invariant: I (n) is “Both a and A are even integers or both are odd integers and a ≥ −1.”

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