Prove each statement using either weak, strong, or structural induction. Make sure to clearly indicate thedifferent parts of your proof: the basis step, the inductive hypothesis, what you will show in the inductivestep, and the inductive step. Make sure to clearly format your proofs and to write in complete, clearsentences.EXAMPLE: Prove that for any nonnegative integer n, Σ i = (n+1)Answer:Proof. (by weak induction)Basis step: n = 1Σ=11(1+1)==1Therefore, (n+1) when n = 1.=Inductive hypothesis: Assume thatInductive step: We will show thati=1i=1i== (+1) for some integer k > 1.i= (k+1)((k+1)+1)k+1Σ=Σ+ (κ + 1)i=1By inductive hypothesis,k+1ΣIMEi=1k(k+1)=+k+12k(k+1)+2(k+1)=2(k+2)(k+1)=2(k+1)((k+1)+1)2Therefore, by weak induction, we have shown that = (n+1) for all nonnegative integers n. Prove that 9" 2" is divisible by 7 for all positive integers n.

Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Answered: Prove each statement using either weak,…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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