Write a conditional statement Write the converse inverse and

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

Solution

Conditional statement : If an animal is a cat, then it has four paws.

Converse: If an animal has 4 paws, then it is a cat.

There are other animals that have 4 paws that are not cats, so the converse is false

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Inverse: If an animal is not a cat, then it does not have 4 paws.

There are animals that are not cats that have 4 paws, so the inverse is false.

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Contrapositive: If an animal does not have 4 paws, then it is not a cat; True

Cats have 4 paws, so the contrapositive is true.

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If a statement’s truth value is false, give a counterexample.

If an even number greater than 2 is prime, then 5 + 4 = 8.

An even number greater than 2 will never be prime, so the hypothesis is false. 5 + 4 is not equal to 8, so the conclusion is false. However, the conditional is true because the hypothesis is false.

{Note : If the hypothesis is false, the conditional statement is true, regardless of the truth value of the conclusion}

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