'If it rained last night, the grass would be wet. The grass is wet. Th…

Question

'If it rained last night, the grass would be wet. The grass is wet. Therefore, it rained last night.'
This pattern is

Accepted Answer

D. Affirming the consequent — invalid

If P → Q, and we know Q, we cannot infer P. The grass could be wet from sprinklers, dew or a leak. This is affirming the consequent. Modus ponens (P→Q, P, ∴Q) and modus tollens (P→Q, ¬Q, ∴¬P) are the valid forms.

Answer

Denying the antecedent — invalid

Answer

Modus ponens — valid

Answer

Modus tollens — valid

'If it rained last night, the grass would be wet. The grass is wet. Therefore, it rained last night.' This pattern is