What is the difference between tautology, contradictions and contingencies?

Tautology

Tautology is a proposition whose logical value is always true.

Example:

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

The Proposition (P Λ q) → (p → q) is a tautology, since 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 invalid,since the results with true and false always give false at the end of the column.

The Proposition ~(P ν q) Λ (P Λ Q) is invalid, since the last column of the truth-table has only F.

Contingency

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

Comments

Note that since 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.Vice of language that consists of saying, in various forms, always to same thing: "The usual grammar is a series of vicious circles, an infinite tautology." (João Ribeiro, Cartas Retruidas, p. 45.)

And if you want a more complex explanation on these subjects, I suggest reading this article .

Conclusion

Tautology, contradiction and contingency are important concepts to continue the study of mathematical and computational logic.It is interesting that at the beginning of wanting to learn the art of programming,these logical parts are taught because a good programmer needs logic.