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Zorluk: OrtaForming Contrapositives

The logically valid contrapositive of the statement 'A clinical trial is deemed ethically sound only if it obtains informed consent from all participants and minimizes potential risks' is 'If a clinical trial fails to obtain informed consent from all participants or fails to minimize potential risks, then it is not deemed ethically sound.'

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The original statement translates to 'If a trial is ethically sound, then it has informed consent AND minimized risks.' Forming the contrapositive requires reversing the conditions and negating them. According to De Morgan's laws, negating an 'AND' statement turns it into an 'OR' statement. Therefore, 'If it does not have informed consent OR does not minimize risks, then it is not ethically sound' is the exact logically valid contrapositive.

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1
Identify the sufficient and necessary conditions in the original statement.
Sufficient: A clinical trial is deemed ethically sound. Necessary: It obtains informed consent from all participants AND minimizes potential risks.
The phrase 'only if' introduces necessary conditions, while the subject of the sentence acts as the sufficient condition.
2
Formulate the logical relationship of the original statement.
Ethically sound -> (Informed consent AND Minimizes risks)
To apply formal logic rules accurately, we must translate the English text into conditional notation.
3
Apply the rule of contraposition and De Morgan's laws.
NOT (Informed consent AND Minimizes risks) -> NOT Ethically sound. This simplifies to: (NOT Informed consent OR NOT Minimizes risks) -> NOT Ethically sound.
The contrapositive requires negating and reversing both sides. Negating an 'AND' statement requires changing it to an 'OR' statement.
4
Compare the resulting logical formulation to the proposed contrapositive in the stem.
The proposed contrapositive matches the derived logical formulation perfectly.
To determine if the statement is true, the proposed text must reflect the exact logical equivalent.

Anahtar Kavram

Forming Contrapositives with Compound Conditionals
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Konular

Forming Contrapositives

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