Exercise5: Define a set X recursively as follows B: 5 EX R: if x EX then x + 10 € X R2: If x EX then x² EX Show by induction that every element of X is divisible by 5.
Exercise5: Define a set X recursively as follows B: 5 EX R: if x EX then x + 10 € X R2: If x EX then x² EX Show by induction that every element of X is divisible by 5.
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 43E
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![Exercise5: Define a set X recursively as follows
B: 5 EX
R: if x EX then x + 10 € X
R2: If x E X then x² EX
Show by induction that every element of X is divisible by 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e7d6a85-60ff-405a-9627-2fb24737f7e4%2Fc0767680-6c5d-402c-be83-d5341b91cff8%2Flunctnj_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise5: Define a set X recursively as follows
B: 5 EX
R: if x EX then x + 10 € X
R2: If x E X then x² EX
Show by induction that every element of X is divisible by 5.
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