

Sample sentences AND operator IF/THEN operator NOT operator OR operator XOR operator Chain Rule Conjunctive Addition Contrapositive DeMorgan's Law Disjunctive Addition Disjunctive Inference Disjunctive Infer. (XOR) Double Negation Modus Ponens Modus Tollens Mutual Exclusion Simplification 2step 3step 4step 5step or more Bad Argument 
Double Negation Double negation is a rule of inference pertaining to the NOT operator. Double negation states that when two NOT operators are applied to a statement, the statement's truth value remains the same. Informally, we say that two NOT operators cancel each other out, leaving the statement they have been applied to unchanged. Imagine we are given a statement: "Today is a cold day." If we apply two NOT operators to it, we obtain "It is not true that today is not a cold day." This is a very complicated way of saying "Today is a cold day." The meaning of the sentence did not change. Formally, we would write: ~~p: "It is not true that today is not a cold day." The statement ~~p is above the line of dashes, and the conclusion p obtained by applying the Double Negation rule is below the line.
Other examples of Double Negation ~~A: "It is not true that the play was not fascinating." ~~X: "It is not true that Christmas is not our favorite
holiday."
Links to Relevant Problems These are links to validity proof problems whose solutions contain Double Negation.
