What is the not symbol in math?

The "not" symbol in mathematics, used to denote negation, can be represented by several common symbols: the exclamation mark (!), the negation sign (¬), and the tilde (~). These symbols are fundamental in mathematical logic, indicating that a statement's truth value is reversed.

Common Symbols for Negation in Mathematics

Here's a breakdown of the symbols frequently used to represent negation in mathematical and logical contexts:

Understanding Negation in Logic

In mathematical logic, negation is a unary operation that takes a proposition P and changes its truth value to the opposite.

• Truth Value Reversal:

  • If a statement P is true, then its negation, ¬P (read as "not P"), is false.
  • If a statement P is false, then its negation, ¬P is true.

• Practical Example:
  Consider the statement P: "The sun is shining."

  • If P is true (the sun is shining), then ¬P (the sun is not shining) is false.
  • If P is false (the sun is not shining), then ¬P (the sun is shining) is true.

These symbols are widely used in propositional logic, Boolean algebra, and computer science to express conditions where a certain state or value is explicitly not met or is the opposite of a given condition.