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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.

Truth Table

PQ  If P then Q


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.