NEGATION APPLIED TO AN ALTERNATION

Let P and Q be sentences which are true or false, but neither of them is both. "Not(P or Q)" means the same thing as "(not(P)) and (not(Q))".

The Negation of an Alternation is equivalent to a Conjunction of the Negations of the alterns
P Q P or Q not(P or Q) not(P) not(Q) (not(P)) and (not(Q))
T T T F F F F
T F T F F T F
F T T F T F F
F F F T T T T



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.