# Tautology

From Encyclopedia of Mathematics

A formula of the language of propositional calculus taking the truth value "true" independently of the truth values "true" or "false" taken by its propositional variables. Examples: , , .

In general one can check whether a given propositional formula is a tautology by simply examining the finite set of all combinations of values of its propositional variables.

#### Comments

#### References

[a1] | Yu.I. Manin, "A course in mathematical logic" , Springer (1977) pp. 31, 54 (Translated from Russian) |

**How to Cite This Entry:**

Tautology. V.N. Grishin (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Tautology&oldid=16024

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098