Editing If and only if (section)

==Definition==

{{multiple image
 | align = right | perrow = 2 | total_width = 200
 | image1 = Venn1000.svg | caption1 = <math>\neg P \and \neg Q</math>
 | image2 = Venn0001.svg | caption2 = <math>P \and Q</math>
 | image3 = Venn1011.svg | caption3 = <math>P \rightarrow Q</math>
 | image4 = Venn1101.svg | caption4 = <math>P \leftarrow Q</math>
 | image5 = Venn1001.svg | caption5 = <math>P \leftrightarrow Q</math>
}}

The [[truth table]] of ''P'' <math>\leftrightarrow</math> ''Q'' is as follows:<ref>[http://www.wolframalpha.com/input/?i=p+%3C%3D%3E+q p <=> q] {{Webarchive|url=https://web.archive.org/web/20161018212628/http://www.wolframalpha.com/input/?i=p+%3C%3D%3E+q |date=18 October 2016 }}. [[WolframAlpha]]</ref><ref>{{citation |title=If and only if |publisher=UHM Department of Mathematics |url=http://www.math.hawaii.edu/~ramsey/Logic/Iff.html |quote=Theorems which have the form "P if and only Q" are much prized in mathematics. They give what are called "necessary and sufficient" conditions, and give completely equivalent and hopefully interesting new ways to say exactly the same thing. |access-date=16 October 2016 |archive-date=5 May 2000 |archive-url=https://web.archive.org/web/20000505112920/http://www.math.hawaii.edu/~ramsey/Logic/Iff.html |url-status=live }}</ref>

{{2-ary truth table|A=P|B=Q
|1|0|0|0|<math>\neg P \and \neg Q</math>
|
|0|0|0|1|<math>P \and Q</math>
|thick
|1|1|0|1|<math>P \rightarrow Q</math>
|
|1|0|1|1|<math>P \leftarrow Q</math>
|thick
|1|0|0|1|<math>P \leftrightarrow Q</math>
}}

It is equivalent to that produced by the [[XNOR gate]], and opposite to that produced by the [[XOR gate]].<ref>{{Cite web|url=http://www.cburch.com/logisim/docs/2.1.0/libs/gates/xor.html|title=XOR/XNOR/Odd Parity/Even Parity Gate|website=www.cburch.com|access-date=2019-10-22|archive-date=7 April 2022|archive-url=https://web.archive.org/web/20220407061623/http://www.cburch.com/logisim/docs/2.1.0/libs/gates/xor.html|url-status=live}}</ref>