https://bsccs.stoney-wiki.com/w/index.php?action=history&feed=atom&title=Tautologies_and_contradictions 2026-05-04T20:12:10Z Revision history for this page on the wiki MediaWiki 1.39.6 https://bsccs.stoney-wiki.com/w/index.php?title=Tautologies_and_contradictions&diff=46&oldid=prev 2025-10-20T13:32:23Z

<p>Created page with &quot;= Tautologies and contradictions = Tautologies and contradictions are special types of logical formulas that are always true or always false, regardless of the truth values of their components. == Tautologies == A tautology is a statement that evaluates to true under all possible interpretations. Tautologies are useful in proofs and as logical identities. === Examples === * p ∨ ¬p (Law of excluded middle) * (p → q) ∨ (q → p) * (p ∨ q) → (q ∨ p)...&quot;</p> <p><b>New page</b></p><div>= Tautologies and contradictions =<br /> <br /> Tautologies and contradictions are special types of logical formulas that are always true or always false, regardless of the truth values of their components.<br /> <br /> == Tautologies ==<br /> A tautology is a statement that evaluates to true under all possible interpretations. <br /> Tautologies are useful in proofs and as logical identities.<br /> <br /> === Examples ===<br /> * p ∨ ¬p (Law of excluded middle) <br /> * (p → q) ∨ (q → p) <br /> * (p ∨ q) → (q ∨ p)<br /> <br /> == Contradictions ==<br /> A contradiction is a statement that evaluates to false under all possible interpretations. <br /> Contradictions represent impossible situations.<br /> <br /> === Examples ===<br /> * p ∧ ¬p (Law of non-contradiction) <br /> * (p ∧ q) ∧ ¬(p ∧ q) <br /> * (p → q) ∧ (p → ¬q) ∧ p<br /> <br /> == Mixed Example ==<br /> Some formulas are neither tautologies nor contradictions but depend on the truth values of their components. <br /> For instance, p ∧ q can be true or false depending on &#039;&#039;p&#039;&#039; and &#039;&#039;q&#039;&#039;.<br /> <br /> == Truth Table Illustration ==<br /> {| class=&quot;wikitable&quot;<br /> ! p !! ¬p !! p ∨ ¬p (tautology) !! p ∧ ¬p (contradiction)<br /> |-<br /> | T || F || T || F<br /> |-<br /> | F || T || T || F<br /> |}<br /> <br /> [[Category:Propositional logic (Aussagenlogik)]]<br /> [[Category: Diskrete Mathematik I (BZG1155pa) 25/26]]</div>

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