|P||Q||if P, then Q||not(if P, then Q)||not(Q)||P and (not(Q))|
Some people understand this principle as follows. They know that "if P, then Q" is false only when the promise is broken---that is, when P is true and Q is false. Q being false makes "not(Q)" true. So, both P and "not(Q)" are true. This is what is meant by "P and (not(Q))".
The truth table to the right is a different approach to the same
principle. Note that columns 4 and 6 have the same truth values.