"Not" of An "Or" (original) (raw)
"NOT" APPLIED TO AN "OR" SENTENCE
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))".
"Not" Applied To An "Or" Sentence
| 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.