Question

If p is true and ~q is false, then p —> ~q is ____ false.

1. Always
2. Sometimes
3. Never

Answer 1

The statement p --> ~q is sometimes false, given that p is true and ~q is false because the conditional statement is only false when its antecedent is true and its consequent is false.

Step-by-step explanation:

In propositional logic, a conditional statement p —> ~q translates to 'if p then not q.' The statement is false only if p is true and ~q is false because a conditional is false only when the antecedent (p) is true and the consequent (~q) is false. Since the problem provides that p is true and ~q is false, which translates to q being true, this means that we have a true antecedent and a false consequent. Therefore, according to the rules of logic, the conditional statement p —> ~q is false.

The direct answer to the question is that p —> ~q is conditionally false based on the values described (p being true and ~q being false). We can accurately say that the conditional will be false in this specific scenario, but not in every possible scenario. Hence, the statement p —> ~q is sometimes false, based solely on the conditions described here.