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LOGICAL OPERATORS

RULES OF LOGIC

VALIDITY PROOFS

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
DeMorgan's Law