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.

Theproposition(pΛq)→(p→q)isatautology,sincethelastcolumnofthetruthtableonlyhasV.

Contradiction

  

Contradictionisapropositionwhoselogicalvalueisalwaysfalse.

ThepropositionpΛ(~p)iscontraválida,becausetheresultswithtrueandfalsealwaysgivefalseattheendofthecolumn.

Theproposition~(pνq)Λ(pΛq)iscontraválida,sincethelastcolumnofthetruthtableonlyhasF.

Contingency

  

Whenapropositionisneithertautologicalnorcontraválida,wecallitcontingencyorcontingentpropositionorindeterminateproposition.

Notes

  

NotethatsinceatautologyisalwaysTrue,itsnegationwillalwaysassumethelogicalvalueofFalsehood,thusresultinginacontradiction.

    

Aboutthewordtautology:

    

1.Voiceoflanguagethatconsistsinsaying,byvariousforms,alwaysthe  samething:  "The usual grammar is a series of vicious circles, an infinite tautology."   (João Ribeiro, Letters Returned, page 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 for us to pursue in the study of mathematical and computational logic. It is interesting that at the beginning of wanting to learn the art of programming, let these logical parts be taught because a good programmer needs logic.