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I have the question: "Translate the following argument into the language of predicate logic. Determine if it is valid or invalid. Justify your answer by providing either an interpretation or a proof. All babies are illogical and nothing that is despised can manage a crocodile. Not all illogical things are despised, therefore some baby can manage some crocodile."

I have it translated in a way that I think is correct with $$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \\(∃x~(Ix → Dx))\\ \therefore~(∃x~(Bx → Mc))$$

I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.

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    $\begingroup$ Your "translation" would be easier to follow if you explained what the predicate symbols stand for. $\endgroup$ – hardmath Dec 5 '18 at 4:39
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You want the second to say "There is an illogical thing and it is not despised."

Also the third should likewise say "There is a baby and it can manage crocodiles."

Remember, existential are restricted by a conjunction. Universals are restricted by a conditional.

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