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Conditional (if-then)

Any two propositions P and Q can be joined by a conditional operator, producing the new, complex, proposition:

If P then Q

The proposition If P then Q is true if and only if either P is false or Q is true. It is false only when P is true and Q is false.

Examples
P Q   If P then Q
T T   T
T F   F
F T   T
F F   T
Comment
A special conditional occurs if we flip the P and Q around: we get if Q then P, which is the same as saying P only if Q.

About Stephen Downes

Many kudos are owed to Stephen Downes, the logician who originally authored this list of fallacies and made it freely available on the Web. His basic structure remains. A mirror of Downes' original site can be found here.