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Give an example of two statements for which the Law of Detachment does not apply.

a. p→q
b. p
c. q
d. The Law of Detachment applies to all cases.

1 Answer

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Final answer:

The Law of Detachment does not apply in situations when only p→q is known without confirmation of p, or when q is presented without information about p.

Step-by-step explanation:

The Law of Detachment, in propositional logic, says that if the statement p→q is true, and p is true, then q must also be true. However, there are situations where the Law of Detachment does not apply, such as:

If we only know that p→q is true, but we do not know whether p is true or false, we cannot conclude q.

Similarly, if we have the statement q, it does not imply that p is true, even if p→q is known to be true. This is not an application of the Law of Detachment but rather affirming the consequent, a logical fallacy.

It is crucial to satisfy both initial conditions: the truth of p→q, and the truth of p, to apply the Law of Detachment.

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