Explanation Given information: loop: while (m = 0 and m = 100 ) m := m + 1 n := n - 1 end while predicate: m + n = 100 Calculation: Let P ( q ) be “ m + n = 100 is true on the qth iteratino of the while-loop”. And let m + n = 100 be true before entry to the loop. Basis step q = 0 : At the 0 th iteration of the while-loop, m + n = 100 is true (as it is true before entry to the loop). Thus P ( 0 ) is true. Inductive step: Let P ( k ) be true, thus m + n = 100 is true on the kth iteration of the while-loop. We need to prove that P ( k + 1 ) is true. On the ( k + 1 ) th iteration, m is increased by 1 and and n is decreased by 1

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ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 5.5, Problem 1ES

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Show that if the predicate is true before entry to the loop, then it is also true after exit from the loop.

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Chapter 5.5, Problem 4TY

Chapter 5.5, Problem 2ES

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To prove: Show that if the predicate is true before entry to the loop, then it is also true after exit from the loop.

Solution Summary: The author demonstrates that if the predicate is true before entry to the loop, then it's also true after exit.