You can determine whether a syllogism is valid or not by applying 3 rules. But first, make sure that it is a syllogism.  Does it have 3 standard-form categorical claims and no more than 3 claims?  Does it use 3 terms and no more than 3 terms?

Two  more concepts to understand before we can apply the rules:

The middle term of a syllogism is the term that appears in both premises but not in the conclusion.

A distributed term means the term says something about every member of the class the term names.

In an A-claim, the S is distributed:
All S are P.
In an E-claim, the S and P are distributed:
No S are P.
In an I-claim, neither S nor P are distributed:
Some S are P.
In an o-claim, the P is distributed:
Some S are not P.
 
mnemonic :   Unprepared Students Never Pass. 
                            Universals = S terms distributed
                            Negatives = P terms distributed
 
 
 

Rules Method of Determining Validity
--Part Two

A syllogism is valid if
 

1. The number of negative claims in the premises are the same as the number of negative claims in the conclusion (no valid syllogism has two negative premises)
2. At least one premise distributes the middle term.
3. Any term distributed in the conclusion must be distributed in its premises

Examples:

 All pianists are keyboard players
Some keyboard players are not percussionists.
Some pianists are not percussionists.

No dogs up for adoption at the animal shelter are pedigreed dogs.
Some pedigreed dogs are expensive dogs.
Some dogs up for adoption at the animal shelter are expensive dogs.
 

No mercantilists are large landowners.
All mercantilists are creditors.
No creditors are large landowners.

All three are invalid.  Which rules do they break?