If p implies q and p is true, what can we conclude about q?

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Multiple Choice

If p implies q and p is true, what can we conclude about q?

The key idea is how implication works in logic. If p implies q and p is true, then q must be true. This is the standard inference rule: from p and p → q, you can conclude q. Think of it as a condition that guarantees a result—once the condition holds, the result follows. So, since p is true and p → q is given, q cannot be false or undetermined; it must be true. The other options would contradict the definite link provided by the implication when the antecedent is actually true.

The key idea is how implication works in logic. If p implies q and p is true, then q must be true. This is the standard inference rule: from p and p → q, you can conclude q. Think of it as a condition that guarantees a result—once the condition holds, the result follows.

So, since p is true and p → q is given, q cannot be false or undetermined; it must be true. The other options would contradict the definite link provided by the implication when the antecedent is actually true.

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