Contrapositive and Converse of a Statement

The video tutorial explores the relationships between conditional statements, contrapositive, and converse. It explains how to identify antecedents and consequents in these statements and discusses their logical equivalence. Examples are provided to illustrate the truth values of these statements, emphasizing that while contrapositive statements are logically equivalent to their original conditionals, converse statements are not.

What is the relationship between statement two and statement one?

• Statement two is the converse of statement one.

• Statement two is the inverse of statement one.

• Statement two is the contrapositive of statement one.

• Statement two is unrelated to statement one.

How is the contrapositive of a conditional statement formed?

• By affirming both the antecedent and the consequent.

• By negating the consequent and then the antecedent.

• By switching the antecedent and the consequent.

• By negating both the antecedent and the consequent.

What is the contrapositive of the statement: 'If a person is happy, then he is in good health'?

• If a person is happy, then he is not in good health.

• If a person is not in good health, then he is not happy.

• If a person is not happy, then he is not in good health.

• If a person is in good health, then he is happy.

What is the converse of the statement: 'If X is a prime number, then X is odd'?

• If X is a prime number, then X is not odd.

• If X is not odd, then X is not a prime number.

• If X is odd, then X is a prime number.

• If X is not a prime number, then X is not odd.

Which statement is logically equivalent to the original conditional statement?

• None of the above.

• The contrapositive statement.

• The inverse statement.

• The converse statement.

Why is the converse of a conditional statement not always true?

• Because it switches the antecedent and consequent.

• Because it negates both the antecedent and consequent.

• Because it affirms both the antecedent and consequent.

• Because it is always true.

What can be concluded about the truth value of a contrapositive statement?

• It is always true.

• It is unrelated to the original statement.

• It is always false.

• It is logically equivalent to the original statement.