Browse Questions

# Write the converse and contra positive of the statement "A positive integer is prime only if it has no divisors other than 1 and itself."

Toolbox:
• Converse of the statement "If $p$ then $q$." is "If $q$ then $p$."
• Contra positive of the statement "If $p$ then $q$" is " If ~ $q$ then ~ $p$."
The given statement is
"A positive integer is prime only if it has no divisors other than 1 and itself."
This statement can be written as
If a positive integer has no divisors other than 1 and itself then it is prime.
Here $p$ : A positive integer has no divisors other than 1 and itself.
$q$ : The integer is prime.
~ $p$ : A positive integer has divisors other than 1 and itself.
~ $q$ : The integer is not prime.
The converse of the given statement is
If $q$ then $p$.
i.e., If a positive integer is prime then it has no divisors other than 1 and itself.
The contra positive of the given statement is
If a positive integer is not prime then it has divisors other than 1 and itself.