I trust every animal that belongs to me.
Dogs gnaw bones.
I admit no animals into my study unless they beg when told to do so.
All the animals in the yard are mine.
I admit every animal that I trust into my study.
The only animals that are really willing to beg when told to do so are dogs.
All the animals in the yard gnaw bones.

The following sorites are taken from Lewis Carroll’s Symbolic Logic. All are valid. Rewrite each sorites in standard form, using letters to represent the terms and reducing the number of terms whenever necessary. Then use Venn diagrams or the rules method to prove each one valid.