Some college students purchase their term papers.
Any cheat is expelled from college.
No one will achieve his career goals who is expelled.
No one who purchases term papers is other than a cheat.
Some college students will not achieve their career goals.

The following sorites 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.