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LOGIC MAIN PAGE

LOGICAL OPERATORS

Sample sentences
AND operator
IF/THEN operator
NOT operator
OR operator
XOR operator

RULES OF LOGIC

Chain Rule
Conjunctive Addition
Contrapositive
DeMorgan's Law
Disjunctive Addition
Disjunctive Inference
Disjunctive Infer. (XOR)
Double Negation
Modus Ponens
Modus Tollens
Mutual Exclusion
Simplification

VALIDITY PROOFS

2-step
3-step
4-step
5-step 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.

p
~p
T
F
F
T

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