All my sons are slim.
No child of mine is healthy who takes no exercise.
All gluttons who are children of mine are fat.
No daughter of mine takes any exercise.
All gluttons who are children of mine are unhealthy.

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.