A set S consists of strings obtained by juxtaposing one or more copies of 1110 and 0111. Use mathematical induction to prove that for every integer n ≥ 1, if s is any string in S that has length 4n, then the number of 1's in s is a multiple of 3.
A set S consists of strings obtained by juxtaposing one or more copies of 1110 and 0111. Use mathematical induction to prove that for every integer n ≥ 1, if s is any string in S that has length 4n, then the number of 1's in s is a multiple of 3.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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Use the definition of string and string length from page 13 in Section 1.4. Recursive definitions for these terms are given in Section 5.9.
A set S consists of strings obtained by juxtaposing one or more copies of 1110 and 0111. Use mathematical induction to prove that for every integer
n ≥ 1,
if s is any string in S that has length 4n, then the number of 1's in s is a multiple of 3.Proof (by mathematical induction): Let
P(n)
be the following sentence.If s is any string in S that has length
4n,
then the number of 1's in s is a multiple of 3.We will show that
P(n)
is true for every integer
n ≥ 1.
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