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Conditional

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.

The truth table for P or Q is as follows:

If you have Java, try it out for yourself:

Set the truth values for the propositions P and Q by clicking on the appropriate button beside "P" and "Q" respectively. What is the truth value of If P then Q? Find out by clicking on the "Compute" button.

P is: T F Q is: T F
Thus, If P then Q is:
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.

What is the truth value of P only if Q? Find out by clicking on the "Compute" button.

P is: T F Q is: T F
Thus, P only if Q is:
Notice that P only if Q is false only when Q is true and P is false.

17 August 1996