In exercise, reorder the premises in each of the arguments to show that the conclusion fol...

In exercise, reorder the premises in each of the arguments to show that the conclusion follows as a valid consequence from the premises. It may be helpful to rewrite the statements in if-then form and replace some statements by their contrapositives. Exercise are adapted from Symbolic Logic by Lewis Carroll.*

Exercise

1. I trust every animal that belongs to me.

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2. Dogs gnaw bones.

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3. I admit no animals into my study unless they will beg when told to do so.

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4. All the animals in the yard are mine.

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5. I admit every animal that I trust into my study.

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6. The only animals that are really willing to beg when told to do so are dogs.

∴ All the animals in the yard gnaw bones.