# Negation

Pronunciation: /nɪˈgeɪ.ʃən/ Explain

A¬A
truefalse
falsetrue
Table 1: Negation truth table.

Negation is an unary operation that changes the truth value of a logical object.[2] If the value is true, negation changes the value to false. If the value is false, negation changes the value to true.

The negative of a negative of a proposition, called a double negative, is equal to the original proposition: .[3] This means that a double negative can be eliminated from a proposition without changing the truth value of the proposition.

### Notation

There are a number of different ways to write negation. See table 2.

NotationPronouncedDescription
¬A 'not A'This notation is used in mathematics. Since it is not found on a standard computer keyboard, one of the other notations are usually substituted for non-professional publications.
~A'not A'This notation is used in mathematics.
NOT A'not A'This notation is used in mathematics. Either ¬A or ~A are preferred.
A 'bar A' This notation is used in mathematics.
A''A prime' or 'A complement'This notation is often used in set theory.
!A'bang A' This notation is used in most computer languages and some mathematics software.
.not. A'not A' This notation is used in the computer language fortran.
Table 2: Negation notation.

### References

1. McAdams, David E.. All Math Words Dictionary, negation. 2nd Classroom edition 20150108-4799968. pg 122. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Couturat, Louis. The Algebra of Logic. Sec 0.15 pg 17. Translated by Lydia Gillingham Robinson, B. A.. Open Court Publishing. 1914. Last Accessed 9/5/2018. http://www.gutenberg.org/files/10836/10836-pdf.pdf. Buy the book
3. Couturat, Louis. The Algebra of Logic. Sec 0.17 pg 19. Translated by Lydia Gillingham Robinson, B. A.. Open Court Publishing. 1914. Last Accessed 9/5/2018. http://www.gutenberg.org/files/10836/10836-pdf.pdf. Buy the book
4. Cupillari, Antonella. Nuts and Bolts of Proof: An Introduction to Mathematical Proofs. 3rd edition. pp 25-34. Academic Press. August 15, 2005. Last Accessed 9/5/2018. Buy the book

McAdams, David E. Negation. 4/26/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/n/negation.html.

### Revision History

4/26/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)