### Negation

"There is a computer in my office." Following logical convention we will represent the above simple, atomic proposition with a single letter:

- C = "There is computer in my office."

C asserts the true fact that there is indeed a computer in my office. It could well be that C is false. (If the computer had been removed from my office.)

- There are various ways of saying that C is not true:
  - "There is no computer in my office."
  - "It is not the case that there is a computer in my office."

(a) and (b) are called the denial of C.

- So the negation of C is:
  - "It is not the case that C."

If we replace 'it is not the case that' with the single symbol: '~'

- Then the denial of C can be symbolized:
  - ~C

If C is true (there is a computer in my office), then ~C (it is not the case that there is a computer in my office) is false. Negation can be thought of as a function since it outputs a truth value for the negation based on the truth value of the original proposition.

- if C is true, then ~C is false.
- if C is false, then ~C is true.

In logic a function is characterized by a truth table:

NEGATION

INPUT | OUTPUT
--- | ---
P | ~P
T | F
F | T

Examples of negation:

- ~A
- ~(B.~D)
- ~[(X > M) + (O . I)]