https://bsccs.stoney-wiki.com/w/index.php?action=history&feed=atom&title=De_Morgan%27s_lawsDe Morgan's laws - Revision history2026-05-04T20:17:15ZRevision history for this page on the wikiMediaWiki 1.39.6https://bsccs.stoney-wiki.com/w/index.php?title=De_Morgan%27s_laws&diff=40&oldid=prevBfh-sts: Created page with "= De Morgan's laws = De Morgan's laws describe the interaction between negation, conjunction, and disjunction. They provide rules for transforming logical statements into equivalent forms. == Statements == * ¬(p ∧ q) ≡ ¬p ∨ ¬q * ¬(p ∨ q) ≡ ¬p ∧ ¬q == Explanation == Negating a conjunction is equivalent to the disjunction of the negations. Negating a disjunction is equivalent to the conjunction of the negations. These transformations are widely u..."2025-10-20T13:31:02Z<p>Created page with "= De Morgan's laws = De Morgan's laws describe the interaction between negation, conjunction, and disjunction. They provide rules for transforming logical statements into equivalent forms. == Statements == * ¬(p ∧ q) ≡ ¬p ∨ ¬q * ¬(p ∨ q) ≡ ¬p ∧ ¬q == Explanation == Negating a conjunction is equivalent to the disjunction of the negations. Negating a disjunction is equivalent to the conjunction of the negations. These transformations are widely u..."</p>
<p><b>New page</b></p><div>= De Morgan's laws =<br />
<br />
De Morgan's laws describe the interaction between negation, conjunction, and disjunction. <br />
They provide rules for transforming logical statements into equivalent forms.<br />
<br />
== Statements ==<br />
* ¬(p ∧ q) ≡ ¬p ∨ ¬q<br />
* ¬(p ∨ q) ≡ ¬p ∧ ¬q<br />
<br />
== Explanation ==<br />
Negating a conjunction is equivalent to the disjunction of the negations. <br />
Negating a disjunction is equivalent to the conjunction of the negations. <br />
These transformations are widely used in proofs, algebraic simplifications, and computer science.<br />
<br />
== Examples ==<br />
* "It is not the case that (I study AND I work)" <br />
≡ "I do not study OR I do not work". <br />
* "It is not the case that (I travel OR I rest)" <br />
≡ "I do not travel AND I do not rest".<br />
<br />
== Truth Table (First Law) ==<br />
{| class="wikitable"<br />
! p !! q !! p ∧ q !! ¬(p ∧ q) !! ¬p ∨ ¬q<br />
|-<br />
| T || T || T || F || F<br />
|-<br />
| T || F || F || T || T<br />
|-<br />
| F || T || F || T || T<br />
|-<br />
| F || F || F || T || T<br />
|}<br />
<br />
== Truth Table (Second Law) ==<br />
{| class="wikitable"<br />
! p !! q !! p ∨ q !! ¬(p ∨ q) !! ¬p ∧ ¬q<br />
|-<br />
| T || T || T || F || F<br />
|-<br />
| T || F || T || F || F<br />
|-<br />
| F || T || T || F || F<br />
|-<br />
| F || F || F || T || T<br />
|}<br />
<br />
[[Category:Propositional logic (Aussagenlogik)]]<br />
[[Category: Diskrete Mathematik I (BZG1155pa) 25/26]]</div>Bfh-sts