5. Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value of each. If a statement's truth value is false, give a counterexample.

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Elaina Caldwell

Mathematics

27 October, 21:24

5. Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value of each. If a statement's truth value is false, give a counterexample.

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Cole Flynn · Answer 1

Conditional Statement: If it is a beagle, it is a dog.

Converse: If it is a dog, it is a beagle. This is a false statement, since a dog can be any other breed (ex. Pomeranian).

Inverse: If it is not a beagle, it is not a dog. Again a false statement, since if it is a different breed, it is a dog despite not being a beagle. For example, it could be a Pomeranian.

Contrapositive: If it not a dog, it is not a beagle. This is true, since if something is not a dog, it won't be any particular breed of dog either (and it won't be a beagle).