Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 5 - Section 5.3 - Recursive Definitions and Structural Induction - Exercises - Page 360: 57

Answer

P(n) is true for all integers n.

Work Step by Step

Let P(n) be “F(n) is well-defined.” Then P(0) is true because F(0) is specified. --Assume that P(k) is true for all k < n. - Then F(n) is well-defined at n because F(n) is given in terms of F(0), F(1), . . . , F(n − 1). -So P(n) is true for all integers n.
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