Weight-ordering logic: Rover weighs less than Fido, and Rover weighs more than Boomer; determine whether the conclusion "Of the three dogs, Boomer weighs the least" must logically follow from the two given premises.
Logical Reasoning
Logical Problems
Difficulty: Easy
Choose an option
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ADefinitely true
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BDefinitely false
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CCannot be determined from the given premises
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DTrue only if Fido is the heaviest
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ETrue only if all three have distinct weights
Answer
Correct Answer: Definitely true
Explanation
Given data
- Premise 1: Rover < Fido.
- Premise 2: Rover > Boomer.
- Claim: Boomer is the lightest of the three (i.e., Boomer < Rover and Boomer < Fido).
Concept / ApproachChain the inequalities to find a strict ordering.
Step-by-step reasoningStep 1: From Premise 2, Boomer < Rover.Step 2: From Premise 1, Rover < Fido.Step 3: Combine the two: Boomer < Rover < Fido. This establishes a strict ascending order of weights.Step 4: Therefore Boomer is lighter than Rover and also lighter than Fido, so Boomer is the least.
Verification / Alternative viewAny numeric assignment respecting the premises (e.g., Boomer=10, Rover=12, Fido=14) makes the conclusion true. There is no counterexample consistent with the premises.
Common pitfalls
- Overthinking ties: the strict inequalities ("less than", "more than") already exclude equality.
Final AnswerDefinitely true.