Question

write the inverse, converse, and contrapositive of the following statement. if a number id prime, then it only has risk factors of 1 and itself

Answer 1

To write the inverse, converse, and contrapositive of the statement 'If a number is prime, then it only has factors of 1 and itself,' the inverse is 'If a number is not prime, then it does not only have factors of 1 and itself,' the converse is 'If a number only has factors of 1 and itself, then it is prime,' and the contrapositive is 'If a number does not only have factors of 1 and itself, then it is not prime.'

Step-by-step explanation:

To write the inverse, converse, and contrapositive of the given statement, we will first clarify the original statement: "If a number is prime, then it only has risk factors (should be 'factors') of 1 and itself." Now, let's construct each of the required statements.

Inverse

If a number is not prime, then it does not only have factors of 1 and itself.

Converse

If a number only has factors of 1 and itself, then it is prime.

Contrapositive

If a number does not only have factors of 1 and itself, then it is not prime.

It is important to note that only the contrapositive and the original statement are always logically equivalent.