(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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4f3c4ec-fe5b-4d14-92c7-f03ecdbdce74%2F9bbd1acf-bafd-4126-ab48-660458ddffb1%2Fhfzd4wd_processed.jpeg&w=3840&q=75)
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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