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Zorluk: KolayMust Be True Questions

In the Highland Reserve, every adult male deer has antlers. Furthermore, any deer with antlers sheds them during the winter season. Some adult male deer in the Highland Reserve are currently tagged with tracking collars.

Based on the information above, which of the following statements must be true? (Select all that apply.)

  1. Every adult male deer in the Highland Reserve sheds its antlers during the winter season.Cevap
  2. At least some deer in the Highland Reserve that are tagged with tracking collars shed their antlers during the winter season.Cevap
  3. C
    Any deer in the Highland Reserve that sheds its antlers during the winter season is an adult male.
  4. D
    Any deer in the Highland Reserve that is not an adult male does not have antlers.
  5. E
    Most deer in the Highland Reserve that are tagged with tracking collars are adult males.

Cevap

The statements that must be true are: 'Every adult male deer in the Highland Reserve sheds its antlers during the winter season' and 'At least some deer in the Highland Reserve that are tagged with tracking collars shed their antlers during the winter season'.
The correct statements are derived from strict logical deductions. The first is a direct transitive chain: if A implies B, and B implies C, then A implies C. Since all adult male deer have antlers, and all deer with antlers shed them, all adult male deer must shed them. The second applies a subset characteristic: since some tagged deer are adult males, and all adult males shed their antlers, those specific tagged deer must also shed their antlers.

Adım Adım Çözüm

1
Analyze the conditional premises
Premise 1: Adult male deer -> has antlers. Premise 2: Has antlers -> sheds them during winter.
Identifying the formal logic relationships is the first step to finding valid deductions.
2
Chain the conditional premises
Adult male deer -> sheds them during winter.
Since 'has antlers' is the necessary condition for the first premise and the sufficient condition for the second, the two statements can be linked to form a new valid deduction.
3
Analyze the quantifier premise
Premise 3: Some adult male deer are tagged with tracking collars.
To find further deductions, we must combine the 'some' statement with the universal conditional statements.
4
Combine the quantifier with the conditional chain
Since at least some adult male deer are tagged, and all adult male deer shed their antlers during winter, it must be true that some tagged deer shed their antlers during winter.
When a subgroup (some tagged deer) belongs to a larger group (adult male deer) that shares a universal characteristic (sheds antlers), that subgroup must also share the characteristic.

Anahtar Kavram

Conditional logic chaining and quantifier intersection
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Must Be True Questions

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