There are eight basic argument forms:
1. Modus Ponens (If P then Q, P, Q) For example, If it’s raining I’ll go to the movies. It’s raining. I’ll go to the movies. I would be lying to you if it were raining and I didn’t go to the movies.
2. Modus Tollens (If P then Q, Not P, Not Q) For example, If you build it they will come. They did not come. You did not build it. I would be lying if they did not come, but you built it.
3. Simplification (P and Q, P) There was an election and John McCain did not win. There was an election. It wouldn’t make sense if I made the first statement and then denied the second statement.
4. Argument by Elimination (Either P or Q, Not P, Q) Either John McCain will win or Barack Obama will win. John McCain did not win. Thus, Barack Obama won. I would be lying if neither one won.
5. Hypothetical Syllogism (If p then q, if q then r, if p then r) If you do not study you will not pass the test. If you do not pass the test you will not pass the class. If you do not study you will not pass the class. This follows the rules also of 1 and 2.
6. Contraposition (If P then Q, If not Q, then not P). If you study you will pass the class. If you do not pass the class you did not study.
7. Equivalence (P if and only if Q, Not P, Not Q) Jack will fall if and only if Jill comes tumbling after. Jack did not fall. Jill did not come tumbling after.
8. Addition (P. P or Q) The president flies on Air Force One. The president flies on Air Force One or cows jump over the moon. This is only false if The president does not fly on Air Force One.
When studying, also study the invalid argument forms such as affirming the antecedent (P then Q, Q, P) some of the arguments you will analyze on the GRE will have invalid argument forms.