Windiness ordering — Determine if the final comparison is entailed Premise 1: Cloudy days tend to be more windy than sunny days. Premise 2: Foggy days tend to be less windy than cloudy days. Claim (to evaluate): Sunny days tend to be less windy than foggy days.
Logical Reasoning
Logical Problems
Difficulty: Medium
Choose an option
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Atrue
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Bfalse
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Cuncertain
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Dboth true and false
Answer
Correct Answer: uncertain
Explanation
Introduction / Context:We are comparing average windiness across weather types. Two ordered comparisons are given: cloudy vs. sunny, and foggy vs. cloudy. We must decide if these imply a third comparison, sunny vs. foggy, without additional meteorological assumptions.
Given Data / Assumptions:
- Cloudy > Sunny (more windy).
- Foggy < Cloudy (less windy).
- No direct relation between Foggy and Sunny is provided.
- “Tend to” indicates general comparisons, but still used as strict orderings for logic.
Concept / Approach:
- If A > B and C < A, the relation between B and C is not fixed; C could still be greater than, equal to, or less than B.
- Therefore, we cannot assert Sunny < Foggy from the premises alone.
Step-by-Step Solution:
Assign numbers to average windiness: let Sunny = 3.Choose Cloudy = 6 (Cloudy > Sunny). Then Foggy must be less than 6.Case 1: Foggy = 5 → Sunny < Foggy (claim true).Case 2: Foggy = 2 → Sunny > Foggy (claim false). Both satisfy premises, so the claim is undetermined.Verification / Alternative check:
Inequality algebra: from Cloudy > Sunny and Foggy < Cloudy, nothing specifies Foggy vs. Sunny, hence uncertainty.Why Other Options Are Wrong:
true / false: Each can occur under valid assignments; neither is compelled.both true and false: Not applicable to a single scenario; uncertainty reflects multiple possible consistent scenarios.Common Pitfalls:
Assuming an implicit chain Cloudy > Foggy > Sunny without evidence. Only two comparisons are given.Final Answer:
uncertain