What is the difference between Tautology, Contradictions and Contingencies?

Question

Anyone who studies Mathematics or develops algorithms should know that Mathematical Logic is essential for several areas of knowledge, eg: in computing (programming), so I would like to know, what is the difference between Tautology, Contradictions and Contingencies?

Answer 1

Tautology

Tautology is a proposition whose logical value is always true.

Example :

The proposition p (~p) is a tautology, because its logical value is always V, according to the truth-table.

The proposition (p Λ q) (p q) is a tautology, as the last column of the truth-table has only V.

Contradiction

Contradiction is a proposition whose logical value is always false.

The proposition p Λ (~p) is counter-valid, because the results with true and false always give false at the end of the column.

The ~(p ν q) proposition Λ (p Λ q) is counter-valid, since the last column of the truth-table only has F.

Contingency

When a proposition is neither tautological nor countervalid, we call it contingency or contingent proposition or indeterminate proposition.

Remarks

Notice that as a tautology is always True, its denial will always assume the logical value of Falsehood, thus resulting in a contradiction.

About the word tautology :

1.Language addiction that consists in saying, in different ways, always the same thing: "The usual grammar is a series of vicious circles, an infinite tautology." (João Ribeiro, Letters Returned, p. 45.)

And if you’d like a more complex explanation of these matters, this article.

Completion

Tautology, contradiction and contingency are important concepts to continue the study of mathematical and computational logic. It’s interesting that at the beginning of wanting to learn the art of programming,.