Questions: The converse, inverse, and contrapositive of a conditional statement Consider this conditional statement. If a person is a professional athlete, then the person is a professional hockey player. (a) Give the converse of the statement. If (Choose one) then (Choose one) (b) Give the contrapositive of the statement. If (Choose one) then (Choose one) (c) Give the inverse of the statement. If (Choose one) then (Choose one)

The converse, inverse, and contrapositive of a conditional statement Consider this conditional statement. If a person is a professional athlete, then the person is a professional hockey player. (a) Give the converse of the statement. If (Choose one) then (Choose one) (b) Give the contrapositive of the statement. If (Choose one) then (Choose one) (c) Give the inverse of the statement. If (Choose one) then (Choose one)
Transcript text: The converse, inverse, and contrapositive of a conditional statement Consider this conditional statement. If a person is a professional athlete, then the person is a professional hockey player. (a) Give the converse of the statement. If $\qquad$ (Choose one) then $\square$ (Choose one) (b) Give the contrapositive of the statement. If $\square$ (Choose one) then $\square$ (Choose one) (c) Give the inverse of the statement. If $\square$ (Choose one) then $\square$ (Choose one)
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Solution

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Solution Steps

Step 1: Understanding the Conditional Statement

The given conditional statement is:
"If a person is a professional athlete, then the person is a professional hockey player."

Step 2: Formulating the Converse

The converse of a conditional statement is formed by swapping the hypothesis and the conclusion.
Converse: "If a person is a professional hockey player, then the person is a professional athlete."

Step 3: Formulating the Contrapositive

The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then swapping them.
Contrapositive: "If a person is not a professional hockey player, then the person is not a professional athlete."

Step 4: Formulating the Inverse

The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion.
Inverse: "If a person is not a professional athlete, then the person is not a professional hockey player."

Final Answer

(a) Converse: If a person is a professional hockey player, then the person is a professional athlete.
\(\boxed{\text{If a person is a professional hockey player, then the person is a professional athlete.}}\)

(b) Contrapositive: If a person is not a professional hockey player, then the person is not a professional athlete.
\(\boxed{\text{If a person is not a professional hockey player, then the person is not a professional athlete.}}\)

(c) Inverse: If a person is not a professional athlete, then the person is not a professional hockey player.
\(\boxed{\text{If a person is not a professional athlete, then the person is not a professional hockey player.}}\)

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