A conditional is a kind of statement that is made out of two others. The normal form of the statement is "If P then Q." P is the antecendt and Q the consequent. "If P, Q" and "Q, if P" are stylistic variations of "If P then Q".

One thing seems quite clear about conditionals:

If the antecedent is true, and the consequent

false, then the conditional as a whole is false. If

Susan comes to the party, and Michael doesn't

bring the salad, then all of the examples preceding

are false. This is the basis for two clearly valid

rules

of inference:

Modus ponens: From If P, then Q and P, infer Q.

Modus tollens: From If P, then Q and not-Q,

infer not-P.

In symbolic logic a defined symbol (often "R") is

called the conditional. The conditions under which

conditional statements that involve this symbol are

true are stipulated by logicians as follows:

1. Antecedent true, consequent true, conditional

true

2. Antecedent true, consequent false, conditional

false

3. Antecedent false, consequent true, conditional

true

4. Antecedent false, consequent false, conditional

true.