

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 
NOT Operator The logical operator NOT (symbolized ~) is called the negation. The NOT operator negates (inverts) a statement. If a statement is true, it becomes false after the negation. Similarly, if a statement is false, it becomes true. Here is an example: Today is not a hot day. In formal logic, we can assign the letter p to a statement (we can use any other letter that we want to). So, let the statement "Today is a hot day" be p. Now, in order to obtain a new statement, "Today is not a hot day", we have to negate p, or apply the NOT operator to it. This is how it looks: ~p: "Today is not a hot day." This is a logical expression. In this expression, p is negated (inverted) by using the NOT operator.
Truth table for NOT A truth table lists truth values (that is, either true or false) for every possible combination of component values in a logical expression. In order to build a truth table for NOT, we need to consider the simplest example of a negation: ~p: "Today is not a hot day." In formal logic, p can take on two possible values: true or false. Let us list these values in the table and see what happens to them as they are negated.
As we read the table, we see that p changes its value to the opposite as it is negated.
Rules of Negation These are links to specific rules pertinent to the NOT operator. Double Negation
