12. Consider the following (true) claim and two possible proofs.Claim. If n is a positive integer, then n² + 3n+2 is not a prime number.Proof 1. Note that n² + 3n+2= (n + 2)(n+1). Since n 1, we have n + 1 > 1 andn+2 > 1, so n²+3n+2 has at least two divisors other than 1 and is therefore not prime.Proof 2. If n is even then we can write n = 2k for some positive integer k. Thenn² + 3n+2 = 4k² +6k+2 = 2(2k² +3k+1), which is even and greater than 2. Since 2is the only even prime, it follows that n² + 3n+2 is not prime.Which of these proofs are valid (i.e. which of them actually prove the claim)?(a) Both proofs are valid.(b) Proof 1 is valid, but Proof 2 is not.(c) Proof 2 is valid, but Proof 1 is not.(d) Neither proof is valid.Select one alternative:(a)(b)O (c)O (d)[1 mark]

Answer: Option a Both proofs are valid.

Consider the following (true) claim and two possible proofs. Claim. If n is a positive integer, then n² + 3n+2 is not a prime number. Proof 1. Note that n² + 3n+ 2 = (n + 2)(n+1). Since n ≥ 1, we have n+1>1 and n+2 > 1, so n²+3n+2 has at least two divisors other than 1 and is therefore not prime.

Consider the following (true) claim and two possible proofs. Claim. If n is a positive integer, then n² + 3n+2 is not a prime number. Proof 1. Note that n² + 3n+ 2 = (n + 2)(n+1). Since n ≥ 1, we have n+1>1 and n+2 > 1, so n²+3n+2 has at least two divisors other than 1 and is therefore not prime.

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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