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Question
State the converse and contrapositive of each of the following statements:
p: A positive integer is prime only if it has no divisors other than 1 and itself.
Solution
Statement p can be written as follows.
If a positive integer is prime, then it has no divisors other than 1 and itself.
The converse of the statement is as follows.
If a positive integer has no divisors other than 1 and itself, then it is prime.
The contrapositive of the statement is as follows.
If positive integer has divisors other than 1 and itself, then it is not prime.
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