Solve this problem using induction. Part AProve the following theorem using either regular or strong induction.Theorem: Suppose that n ≥ 2 people are at a gathering. Every person shakes hands withevery other person, but not themselves. Then, the number of total handshakes which occur isn(n-1)2Part BIn Part A, did you use regular or strong induction? Describe the specific feature(s) of yourproof that distinguish which one you used.

Answered: Image /qna-images/answer/519b5ef6-5b0c-4189-9382-f45d751377f2.jpg

Answered: Part A Prove the following theorem…

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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Tower of Hanoi The result in Exercise 39 suggest that the minimum number of moves required to transfer n disks from one peg to another is given by the formula 2n1. Use the following outline to prove that this result is correct using mathematical induction. a Verify the formula for n=1. b Write the induction hypothesis. c How many moves are needed to transfer all but the largest of k+1 disks to another peg? d How many moves are needed to transfer the largest disk to an empty peg? e How many moves are needed to transfer the first k disks back onto the largest one? f How many moves are needed to accomplish steps c, d, and e? g Show that part f can be written in the form 2(k+1)1. h Write the conclusion of the proof.
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Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n ≥ 2 people are at a gathering. Every person shakes hands with every other person, but not themselves. Then, the number of total handshakes which occur is n(n-1)