Question

1. given the statement: if you play professional basketball, then you are an athlete. match the alternate forms to their classifications.

draggable item \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tcategory
if you do not play professional basketball, then you are not an athlete. \t→ \tconverse
if you are an athlete, then you play professional basketball. \t→ \tinverse
if you are not an athlete, then you do not play professional basketball. \t→ \tcontrapositive

Explanation:

1. For a conditional statement \( p \to q \) (where \( p \): "you play professional basketball", \( q \): "you are an athlete"):

• Inverse: Negates both \( p \) and \( q \), so \(

eg p \to
eg q \). The statement "If you do not play professional basketball, then you are not an athlete" matches \(
eg p \to
eg q \), so it is the inverse.

• Converse: Swaps \( p \) and \( q \), so \( q \to p \). The statement "If you are an athlete, then you play professional basketball" matches \( q \to p \), so it is the converse.
• Contrapositive: Negates and swaps \( p \) and \( q \), so \(

eg q \to
eg p \). The statement "If you are not an athlete, then you do not play professional basketball" matches \(
eg q \to
eg p \), so it is the contrapositive.

Answer:

• "If you do not play professional basketball, then you are not an athlete." → inverse
• "If you are an athlete, then you play professional basketball." → converse
• "If you are not an athlete, then you do not play professional basketball." → contrapositive