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

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Multiple Choice

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

A conditional statement is false only when the first part is true and the second part is false. Here, the second part (q) is false, so to keep the implication true, the first part (p) cannot be true. In other words, p must be false. If p were true, q would need to be true for the implication to hold, but q is not, which would make the implication false. So p is false.

A conditional statement is false only when the first part is true and the second part is false. Here, the second part (q) is false, so to keep the implication true, the first part (p) cannot be true. In other words, p must be false. If p were true, q would need to be true for the implication to hold, but q is not, which would make the implication false. So p is false.

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