# If the given statement is not in if-then form, rewrite it. Write the converse, inverse, and contra

*label*Mathematics

*timer*Asked: Apr 26th, 2017

**Question description**

If the given statement is not in if-then form, rewrite it. Write the converse, inverse, and contrapositive of the given conditional statement. Determine the truth value of all four statements. If a statement is false, give a counterexample.

Odd natural numbers greater than 6greater than 6 are prime.

give an answer for each one

**Rewrite the given statement in if-then form. Choose the correct answer below.**

Odd natural numbers greater than 6greater than 6 are prime.

A.If an odd natural number is greater than 6greater than 6, then it is prime.

B.If a number is prime, then it is an odd natural number greater than 6greater than 6.

C.If an odd natural number is greater than 6greater than 6, then it is not prime.

D.If a number is not prime, then it is an odd natural number greater than 6greater than 6.

**Determine the truth value of the conditional statement. If the statement is false, give a counterexample. Choose the correct answer below.**

A.False: The number 11 is natural and odd comma but not prime or greater than 6.The number 11 is natural and odd, but not prime or greater than 6.

B.False: The number 10 is natural and greater than 6 comma but not odd or prime.The number 10 is natural and greater than 6, but not odd or prime.

C.True

D.False: The odd natural number 15 is greater than 6 comma but is not prime.The odd natural number 15 is greater than 6, but is not prime.

**Write the converse of the statement. Choose the correct answer below.**

If an odd natural number is not greater than 6greater than 6,**then it is not prime.**

If a number is not prime, then it is an odd natural number greater than 6greater than 6.

If an odd natural number is greater than 6greater than 6,

**then it is prime.**

If a number is prime, then it is an odd natural number greater than 6greater than 6.

**Determine the truth value of the converse. If the statement is false, give a counterexample. Choose the correct answer below.**

**True**

**False: The number 10 is natural and greater than 6 comma but not odd or prime.The number 10 is natural and greater than 6, but not odd or prime.**

**False: The number 11 is natural and odd comma but not prime or greater than 6.The number 11 is natural and odd, but not prime or greater than 6.**

**False: The number 3 is a prime number comma but it is not an odd natural number greater than 6.The number 3 is a prime number, but it is not an odd natural number greater than 6.**

**Write the inverse of the statement. Choose the correct answer below.**

**If an odd natural number is not greater than 6greater than 6,****then it is not prime.**

**If an odd natural number is greater than 6greater than 6,****then it is not prime.**

**If an odd natural number is greater than 6greater than 6,****then it is prime.**

**If an odd natural number is not prime, then it is greater than 6greater than 6.**

**Determine the truth value of the inverse. If the statement is false, give a counterexample. Choose the correct answer below.**

**False: The number 11 is natural and odd comma but not prime or greater than 6.The number 11 is natural and odd, but not prime or greater than 6.**

**False: The number 3 is an odd natural number not greater than 6 comma but it is prime.The number 3 is an odd natural number not greater than 6, but it is prime.**

**False: The number 10 is natural and greater than 6 comma but not odd or prime.The number 10 is natural and greater than 6, but not odd or prime.**

**True**

**Write the contrapositive of the statement. Choose the correct answer below.**

**If a number is not prime, then it is not an odd natural number greater than 6greater than 6.**

**If an odd natural number is not prime, then it is greater than 6greater than 6.**

**If an odd natural number is greater than 6greater than 6,****then it is not prime.**

**If an odd natural number is prime, then it is not greater than 6greater than 6.**

**Determine the truth value of the contrapositive. If the statement is false, give a counterexample. Choose the correct answer below.**

**False: The number 10 is natural and greater than 6 comma but not odd or prime.The number 10 is natural and greater than 6, but not odd or prime.**

**False:****The number 15 is not prime comma but it is an odd natural number greater than 6.The number 15 is not prime, but it is an odd natural number greater than 6.**

**False: The number 11 is natural and odd comma but not prime or greater than 6.The number 11 is natural and odd, but not prime or greater than 6.**

**True:**