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Zorluk: KolayChaining Conditional Statements

Match each set of conditional premises with its logically valid chained conclusion or its valid contrapositive.

  • If the meeting is held, the training is conducted. If the training is conducted, the project is approved.If the meeting is held, the project is approved.
  • If the training is conducted, the review is completed. If the review is completed, the meeting is held.If the meeting is not held, the training is not conducted.
  • If the project is approved, the meeting is held. If the meeting is held, the review is completed.If the project is approved, the review is completed.
  • If the review is completed, the project is approved. If the project is approved, the training is conducted.If the training is not conducted, the review is not completed.

Cevap

The logically valid pairs map each premise set to its direct transitive chain or the contrapositive of that chain.
Each valid pairing is derived by connecting two conditional statements to form a chain (A -> B and B -> C yields A -> C). For two of the pairs, the correct matching item provides the contrapositive of this chain (since A -> C implies ~C -> ~A).

Adım Adım Çözüm

1
Analyze the first set of premises.
Chain: Meeting -> Training -> Project. Direct inference: Meeting -> Project. This matches the item stating 'If the meeting is held, the project is approved'.
Transitive logic allows us to bypass the intermediate necessary condition.
2
Analyze the second set of premises.
Chain: Training -> Review -> Meeting. Direct inference: Training -> Meeting. The contrapositive of this inference is 'Not Meeting -> Not Training'.
If the final necessary condition fails, the initial sufficient condition could not have occurred.
3
Analyze the third set of premises.
Chain: Project -> Meeting -> Review. Direct inference: Project -> Review. This matches the item stating 'If the project is approved, the review is completed'.
Linking the conditions yields a direct forward inference.
4
Analyze the fourth set of premises.
Chain: Review -> Project -> Training. Direct inference: Review -> Training. The contrapositive is 'Not Training -> Not Review'.
Reversing and negating the valid direct chain produces a valid contrapositive.

Anahtar Kavram

Chaining conditional statements and forming contrapositives
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Konular

Chaining Conditional Statements

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