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Zorluk: ZorForming Contrapositives

Under the revised maritime salvage code, a claimant is entitled to a full recovery fee only if the recovered vessel was actively broadcasting a distress signal or the claimant can prove the vessel was abandoned for at least thirty days.

Consider this deduction: 'If a claimant cannot prove the vessel was abandoned for at least thirty days, or if the vessel was not actively broadcasting a distress signal, then the claimant is not entitled to a full recovery fee.'

Is this deduction logically valid based exclusively on the code provided?

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Cevap

False. The deduction is logically invalid due to an incorrect application of De Morgan's laws when forming the contrapositive.
The deduction is logically invalid. The original rule requires at least one of two conditions (broadcasting OR abandoned) to be true for the fee entitlement to be possible. To properly deduce that a claimant is NOT entitled to the fee via a contrapositive, BOTH conditions must be negated and joined by 'AND' (not broadcasting AND not abandoned). The provided statement incorrectly uses 'or', meaning a claimant who only failed one condition would erroneously lose the fee, contradicting the original rule.

Adım Adım Çözüm

1
Identify the conditional indicator and translate the original rule into formal logic.
Entitled to Fee -> (Broadcasting Signal OR Proved Abandoned).
The phrase 'only if' introduces a necessary condition. The condition itself is a compound statement joined by the word 'or'.
2
Formulate the correct contrapositive by negating both sides and reversing their order.
NOT (Broadcasting Signal OR Proved Abandoned) -> NOT Entitled to Fee.
A logically valid deduction via contrapositive requires negating the necessary condition to serve as the new sufficient condition.
3
Apply De Morgan's laws to simplify the negated necessary condition.
(NOT Broadcasting Signal AND NOT Proved Abandoned) -> NOT Entitled to Fee.
The negation of an 'OR' statement is an 'AND' statement. A claimant must fail BOTH conditions to guarantee the loss of the fee.
4
Compare the logically valid contrapositive to the deduction provided in the stem.
The provided deduction uses 'or' (fails condition A OR fails condition B) instead of 'and'.
Because the deduction concludes the fee is denied based on failing only one condition rather than failing both, it is an invalid deduction.

Anahtar Kavram

Forming Contrapositives with De Morgan's Laws
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