https://bsccs.stoney-wiki.com/w/index.php?action=history&feed=atom&title=EquivalenceEquivalence - Revision history2026-05-04T20:10:24ZRevision history for this page on the wikiMediaWiki 1.39.6https://bsccs.stoney-wiki.com/w/index.php?title=Equivalence&diff=29&oldid=prevBfh-sts: Created page with "= Equivalence = Equivalence is the logical operation corresponding to "IF AND ONLY IF". It states that two propositions are logically identical in truth value. == Symbols == * p ↔ q (standard notation) * p ⇔ q (alternative) * p IFF q (short for "if and only if") == Definition == The equivalence ''p ↔ q'' is true if ''p'' and ''q'' have the same truth value. It is false if their truth values differ. == Truth Table == {| class="wikitable" ! p !! q !! p ↔ q..."2025-10-20T13:28:39Z<p>Created page with "= Equivalence = Equivalence is the logical operation corresponding to "IF AND ONLY IF". It states that two propositions are logically identical in truth value. == Symbols == * p ↔ q (standard notation) * p ⇔ q (alternative) * p IFF q (short for "if and only if") == Definition == The equivalence ''p ↔ q'' is true if ''p'' and ''q'' have the same truth value. It is false if their truth values differ. == Truth Table == {| class="wikitable" ! p !! q !! p ↔ q..."</p>
<p><b>New page</b></p><div>= Equivalence =<br />
<br />
Equivalence is the logical operation corresponding to "IF AND ONLY IF". <br />
It states that two propositions are logically identical in truth value.<br />
<br />
== Symbols ==<br />
* p ↔ q (standard notation)<br />
* p ⇔ q (alternative)<br />
* p IFF q (short for "if and only if")<br />
<br />
== Definition ==<br />
The equivalence ''p ↔ q'' is true if ''p'' and ''q'' have the same truth value. <br />
It is false if their truth values differ.<br />
<br />
== Truth Table ==<br />
{| class="wikitable"<br />
! p !! q !! p ↔ q<br />
|-<br />
| T || T || T<br />
|-<br />
| T || F || F<br />
|-<br />
| F || T || F<br />
|-<br />
| F || F || T<br />
|}<br />
<br />
== Examples ==<br />
* If ''p'' = "2 is even" and ''q'' = "4 is divisible by 2", <br />
then ''p ↔ q'' is true, since both are true.<br />
* In Python: <code>p == q</code> (when p and q are booleans)<br />
* In Java: <code>p == q</code> (when p and q are booleans)<br />
<br />
<br />
[[Category:Propositional logic (Aussagenlogik)]]<br />
[[Category: Diskrete Mathematik I (BZG1155pa) 25/26]]</div>Bfh-sts