By giving a counter-example, show that the statement is false :
Question:

By giving a counter-example, show that the statement is false :

p : If n is an odd positive integer, then n is prime.

 

Solution:

Let us take a odd positive integer n = +9

Even though $(+9)$ is an odd positive integer, It is divisible by 3 .

To be a prime number, a number must only have itself and 1 as its factors. Since 9 has 3 as its factor too, it is not a prime number in spite of being an odd positive integer.

$\therefore$ The given statement $p$ is false.

 

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