Soru

Zorluk: OrtaIdentifying Must-Be-True Statements and Valid Deductions

A long-term agricultural study in a semi-arid basin established that whenever seasonal rainfall drops below 250 millimeters, farmers who irrigate their crops using unlined soil canals lose at least 35 percent of their diverted water to seepage. Conversely, any farm in the basin that adopts high-efficiency drip irrigation retains at least 85 percent of its diverted water regardless of seasonal rainfall levels. Last season, seasonal rainfall in the basin was 210 millimeters, yet Farm X lost less than 20 percent of its diverted water.

If the statements above are true, which of the following MUST also be true regarding Farm X last season?

  1. Farm X did not rely on unlined soil canals to irrigate its crops last season.Cevap
  2. B
    Farm X used high-efficiency drip irrigation to irrigate its crops last season.
  3. C
    If Farm X had received more than 250 millimeters of rainfall last season, its diverted water loss would have been greater than 35 percent.
  4. D
    Farm X diverted a greater total volume of water last season than did neighboring farms using unlined soil canals.
  5. E
    Any farm in the basin that loses less than 35 percent of its diverted water during a low-rainfall season must be using high-efficiency drip irrigation.

Cevap

Farm X did not rely on unlined soil canals to irrigate its crops last season.
The correct answer is derived using formal conditional logic. The stimulus establishes that when rainfall is under 250 mm, using unlined soil canals guarantees a water loss of at least 35%. Since the rainfall was 210 mm and Farm X lost less than 20% of its diverted water, Farm X cannot have used unlined soil canals. By contrapositive reasoning, if the outcome (loss ≥ 35%) did not occur despite the trigger condition (rainfall < 250 mm) being met, the requirement for that outcome (unlined soil canals) must have been absent.

Adım Adım Çözüm

1
Analyze the conditional rule for unlined soil canals.
If (Rainfall < 250 mm) AND (Unlined Soil Canals), then (Water Loss ≥ 35%).
This is a direct premise established by the study.
2
Evaluate the conditions given for Farm X last season.
Rainfall was 210 mm (which is strictly less than 250 mm), and Farm X's Water Loss was strictly less than 20%.
These are the explicit facts provided about Farm X.
3
Apply the contrapositive of the conditional rule.
Since Water Loss was NOT ≥ 35% (it was < 20%) while Rainfall was < 250 mm, the condition 'Unlined Soil Canals' must be FALSE for Farm X.
If P and Q imply R, then P and not-R implies not-Q.

Anahtar Kavram

Applying Contrapositive Logic in Must-Be-True Deductions
Bu soruyu puanla