Given the premises a → b , d, d → b and a, consider the following proof of b: 1. a Premise 2. a b Premise. 3. b Modus Ponens 1, 2 The argument is not valid; it doesn't use all the premises O valid not valid because using d and d → b also can be used to derive b, and it is preferable to use the premises first listed. ridiculous O not välid; the shortest possible proof is 4 lines long.

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