Question

What are the converse, inverse, and contrapositive of the following conditional statement? What are the truth values of each?

If today is Sunday, then tomorrow is Monday.

A. Converse: If today is not Sunday, then tomorrow is not Monday. Inverse: If tomorrow is Monday, then today is Sunday. Contrapositive: If tomorrow is not Monday, then today is not Sunday. Only the contrapositive is true.

B. Converse: If today is not Sunday, then tomorrow is not Monday. Inverse: If tomorrow is Monday, then today is Sunday. Contrapositive: If tomorrow is not Monday, then today is not Sunday. All three are true.

C. Converse: If tomorrow is Monday, then today is Sunday. Inverse: If today is not Sunday, then tomorrow is not Monday. Contrapositive: If tomorrow is not Monday, then today is not Sunday. All three are true.

Answer 1

The converse, inverse, and contrapositive of the conditional statement and their truth values.

Step-by-step explanation:

The converse of the conditional statement 'If today is Sunday, then tomorrow is Monday' is 'If today is not Sunday, then tomorrow is not Monday'. The inverse is 'If tomorrow is not Monday, then today is not Sunday'. The contrapositive is 'If tomorrow is not Monday, then today is not Sunday'. A. Converse: If today is not Sunday, then tomorrow is not Monday.

Inverse: If tomorrow is Monday, then today is Sunday.

Contrapositive: If tomorrow is not Monday, then today is not Sunday.

Only the contrapositive is true.

Answer 2

Converse: If tomorrow is Monday, then today is Sunday.

Inverse: If today is not Sunday, then tomorrow is not Monday.

Contrapositive: If tomorrow is not Monday, then today is not Sunday. All three are true.

Thus the correct option is C.

Step-by-step explanation:

The original conditional statement is "If today is Sunday, then tomorrow is Monday." The converse of this statement switches the hypothesis and conclusion, resulting in "If tomorrow is Monday, then today is Sunday."

The inverse negates both the hypothesis and the conclusion to form "If today is not Sunday, then tomorrow is not Monday." The contrapositive combines the inversion and the switching of the hypothesis and conclusion, leading to "If tomorrow is not Monday, then today is not Sunday."

In this scenario, option C correctly identifies the converse, inverse, and contrapositive statements along with their respective truth values. The truth values of these statements are determined by their logical relationships to the original conditional statement.

According to the rules of logical equivalence, the contrapositive always holds true when the original statement is true. Thus, in this case, all three statements (converse, inverse, and contrapositive) are true.

Therefore, the correct option is C.