In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false. If n is even, then n is not prime if n is a square number, then n is not prime if n is a prime number and n ≥ 10, then n+2 is prime or n+4 is prime. A. What two statements are false and in each case give a counter example to show that it is false B. Prove the true statement
In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false. If n is even, then n is not prime if n is a square number, then n is not prime if n is a prime number and n ≥ 10, then n+2 is prime or n+4 is prime. A. What two statements are false and in each case give a counter example to show that it is false B. Prove the true statement
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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Question
In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false.
- If n is even, then n is not prime
- if n is a square number, then n is not prime
- if n is a prime number and n ≥ 10, then n+2 is prime or n+4 is prime.
A. What two statements are false and in each case give a counter example to show that it is false
B. Prove the true statement
Expert Solution
Step 1
A. The 1st and the last statement are false.
Counterexample for the 1st statement : Take n=2 , then n is even as well as prime.
Counterexample for the last statement : Take n=23 ,which is prime number and 23 >= 10 . But neither of (23+2)=25 nor (23+4)=27 is a prime.
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