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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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. 

  • 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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