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Zorluk: KolayDiagramming Conditional Statements

According to the newly published guidelines for the National Architectural Excellence Award, a commercial building is eligible for the highest tier of recognition only if it operates with a net-zero carbon footprint.

Based on the guidelines above, which one of the following statements must be true?

  1. A
    If a commercial building operates with a net-zero carbon footprint, it is eligible for the highest tier of recognition.
  2. B
    If a commercial building is not eligible for the highest tier of recognition, it does not operate with a net-zero carbon footprint.
  3. C
    Operating with a net-zero carbon footprint is a sufficient condition for a commercial building to be recognized at the highest tier.
  4. If a commercial building does not operate with a net-zero carbon footprint, it is not eligible for the highest tier of recognition.Cevap
  5. E
    Most commercial buildings that are not eligible for the highest tier of recognition fail to operate with a net-zero carbon footprint.

Cevap

The statement expressing that if a commercial building does not operate with a net-zero carbon footprint, it is not eligible for the highest tier of recognition.
The stimulus establishes a conditional relationship using the indicator 'only if'. 'Only if' introduces the necessary condition. Therefore, the logical structure is: Eligible for Highest Tier -> Net-Zero Carbon Footprint. The correct answer accurately represents the contrapositive of this relationship: if the necessary condition is not met (No Net-Zero), then the sufficient condition cannot occur (Not Eligible).

Adım Adım Çözüm

1
Identify the conditional indicator and translate the stimulus into formal logic.
The phrase 'only if' introduces a necessary condition. The relationship is: Eligible for highest tier -> Operates with net-zero carbon footprint.
Diagramming the baseline conditional relationship correctly is required to draw valid logical deductions.
2
Form the valid contrapositive of the diagrammed conditional statement.
Negate both sides and reverse the arrow: Does NOT operate with net-zero carbon footprint -> NOT eligible for highest tier.
The contrapositive is logically equivalent to the original statement and is a guaranteed true deduction.
3
Evaluate the answer choices against the valid contrapositive and original statement.
The correct option perfectly matches the contrapositive generated in Step 2.
Valid deductions in formal logic must be completely supported by the premises without assuming outside information or committing formal logical fallacies.

Anahtar Kavram

Translating conditional statements using 'only if' and applying the rule of contraposition.
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Konular

Diagramming Conditional Statements

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