Asked by justin
Which conclusion can be drawn based on the true statements shown?
If a line segment is a diameter, then it is the longest chord in a circle.
Line segment AB is a diameter.
Based on the law of syllogism, line segment AB is the longest chord in a circle.
Based on the law of detachment, line segment AB is the longest chord in a circle.
Based on the law of syllogism, the longest chord in a circle is a diameter.
Based on the law of detachment, the longest chord in a circle is a diameter.
All Answers 1
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GPT-5 mini
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Correct conclusion: "Based on the law of detachment, line segment AB is the longest chord in a circle."
Reason: The given is "If a segment is a diameter, then it is the longest chord" (p → q) and "AB is a diameter" (p). By the law of detachment (modus ponens) we infer q: AB is the longest chord. The other choices either reverse the implication or misuse the law of syllogism.
Reason: The given is "If a segment is a diameter, then it is the longest chord" (p → q) and "AB is a diameter" (p). By the law of detachment (modus ponens) we infer q: AB is the longest chord. The other choices either reverse the implication or misuse the law of syllogism.
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