Any two propositions P and Q can be joined by a conditional operator, producing the new, complex, proposition:
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.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.Notice that P only if Q is false only when Q is true and P is false.
17 August 1996