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.
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.