Question

Look at the following conditionals: If people do not celebrate, then the Polk Rebels do not win the championship. If the Polk Rebels do not win the championship, then people do not celebrate. Is the second conditional the contrapositive, converse, or inverse of the first conditional? contrapositive , converse , inverse

Answer 1

The second conditional is the inverse of the first conditional.

Step-by-step explanation:

The second conditional is the inverse of the first conditional. In a conditional statement, the inverse is formed by negating both the antecedent and the consequent. Let's look at the first conditional:

Conditional 1: If people do not celebrate, then the Polk Rebels do not win the championship.

The inverse of this statement would be:

Inverse of Conditional 1: If people do celebrate, then the Polk Rebels win the championship.

As you can see, the antecedent and consequent have been negated to form the inverse of the first conditional. Therefore, the second conditional is the inverse of the first conditional.

Answer 2

The second conditional is the contrapositive of the first conditional.

The second conditional is the contrapositive of the first conditional.

Here's why:

Contrapositive: In a conditional statement "If P, then Q," the contrapositive is formed by negating both the hypothesis (P) and the conclusion (Q), and reversing their order. It has the form "If not Q, then not P." The contrapositive is logically equivalent to the original statement, meaning they have the same truth value.

Converse: The converse is formed by swapping the hypothesis and conclusion of the original statement. It has the form "If Q, then P." The converse is not logically equivalent to the original statement.

Inverse: The inverse is formed by negating both the hypothesis and conclusion of the original statement, but keeping their order the same. It has the form "If not P, then not Q." The inverse is also not logically equivalent to the original statement.

In this case:

Original conditional: "If people do not celebrate (not P), then the Polk Rebels do not win the championship (not Q)."

Second conditional: "If the Polk Rebels do not win the championship (not Q), then people do not celebrate (not P)."

This fits the pattern of the contrapositive: Negating both the hypothesis and conclusion, and reversing their order.