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(B) If n is a square ser, then is not prime. (C) If n is a prime number and n ≥ 10, then n +2 is or n +4 is prime.

(B) If n is a square ser, then is not prime. (C) If n is a prime number and n ≥ 10, then n +2 is or n +4 is prime.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false. (A) If n! is even, then n is not prime. (B) If n is a square number, then n is not prime. (C) If n is a prime number and n ≥ 10, then n + 2 is prime or n +4 is prime. (a) Write down which two statements are false and in each case give a counter-example to show that it is false. (b) Prove the true statement.
Transcribed Image Text:In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false. (A) If n! is even, then n is not prime. (B) If n is a square number, then n is not prime. (C) If n is a prime number and n ≥ 10, then n + 2 is prime or n +4 is prime. (a) Write down which two statements are false and in each case give a counter-example to show that it is false. (b) Prove the true statement.
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