Valid Forms

1) A Disjunctive Syllogism begins with an “either … or” (disjunctive) statement. The second

premise then negates, or eliminates, one of the disjuncts. As a result, the affirmation of

the second disjunct follows. For example:

Either the battery is dead or there is a short in the ignition.

The battery is not dead.

Therefore, there is a short in the ignition.

The structure of the argument follows the pattern:

Either p or q.

Not p.

Therefore q.

Remember, any argument following this pattern will be valid, regardless of the truth of

the premises.

2) A Hypothetical Syllogism is a series of “if … then” (conditional) statements forming a

chain of reasoning.

If Mary studies, then she will pass the class.

If she passes the class, then she will graduate.

Therefore, if she studies, she will graduate.

The structure of the argument follows the pattern:

If p then q.

If q then r.

Therefore, if p then r.

This pattern is always valid.

Important to note is the type of statements found in Hypothetical Syllogisms as well as many

other arguments. These are conditional statements, usually taking the form, “if … then.” The

first part (after “if”) of the conditional is the antecedent; the second part (after “then”) is the

consequent. The next two valid argument forms are based on the conditional.

3) Modus Ponens (Affirming the Antecedent) follows the pattern:

If p then q.

p.

Therefore, q.

An example:

If we are in Fullerton, then we are in California.

We are in Fullerton.

Therefore, we are in California.

Here we begin with a conditional. Next, we assert the antecedent to be true. It

deductively follows, then that the consequent must be true. Notice in this example that since

both premises are true, the argument is sound. Also remember, even if the remises were not

true, the argument would still be valid.

4) Modus Tollens follows the pattern:

If p then q.

Not q.

Therefore, not p.

An example:

If we are in Fullerton, then we are in California.

We are not in California.

Therefore, we are not in Fullerton.

We begin again with a conditional as the first premise. This time we deny that the

consequent is true. From these premises, we conclude that the antecedent must be false.