Chapter 1, Problem 1ST

To determine

To check:Whether the given statement is True or False.

Explanation of Solution

Given information:

Thegivenstatement is, “Every positive integer is either prime or composite”.

An integer $p$ is called prime provide that $p>1$ and the only positive divisors of $p$ are $1$ and $p$ .

A positive integer $a$ is called composite provided there is an integer $b$ such that $1<b<a$ and $b/a$ .

Integer $1$ is neither a prime nor a composite number, so it is not necessary that every positive integer is either prime or composite.

Hence, the given statement is false.