|P||Q||P or Q||not(P or Q)||not(P)||not(Q)||(not(P)) and (not(Q))|
Some people understand this principle as follows. They know that "P or Q" is false only when both P and Q are false. P being false makes "not(P)" true; Q being false makes "not(Q)" true. So, both "not(P)" and "not(Q)" are true. This is what is meant by "(not(P)) and (not(Q))".
The truth table to the right is a different approach to the same principle. Note that columns 4 and 7 have the same truth values.
This is one of the famous DeMorgan transformations developed by Augustus Demorgan.