Editing Logical biconditional (section)

==Notations==
Notations to represent equivalence used in history include: 
* <math>=</math> in [[George Boole]] in 1847.<ref name="boole1847">{{cite book |last1=Boole |first1=G. |title=The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning |date=1847 |publisher=Macmillan, Barclay, & Macmillan/George Bell |location=Cambridge/London |page=17 |url=https://archive.org/details/mathematicalanal00booluoft}}</ref> Although Boole used <math>=</math> mainly on classes, he also considered the case that <math>x,y</math> are propositions in <math>x=y</math>, and at the time <math>=</math> is equivalence.
* <math>\equiv</math> in [[Gottlob Frege|Frege]] in 1879;<ref name="frege1879b">{{cite book |last1=Frege |first1=G. |title=Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens |date=1879 |publisher=Verlag von Louis Nebert |location=Halle a/S. |page=15 |language=German}}</ref>
* <math>\sim</math> in [[Paul Bernays|Bernays]] in 1918;<ref name="bernays1918">{{cite book |last1=Bernays |first1=P. |title=Beiträge zur axiomatischen Behandlung des Logik-Kalküls |date=1918 |publisher=Universität Göttingen |location=Göttingen |page=3}}</ref>
* <math>\rightleftarrows</math> in [[David Hilbert|Hilbert]] in 1927 (while he used <math>\sim</math> as the main symbol in the article);<ref name="hilbert1927">{{cite journal |last1=Hilbert |first1=D. |title=Die Grundlagen der Mathematik |journal=Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität |orig-date=1927 |date=1928 |volume=6 |pages=65–85 |doi=10.1007/BF02940602 |language=German}}</ref>
* <math>\leftrightarrow</math> in [[David Hilbert|Hilbert]] and [[Wilhelm Ackermann|Ackermann]] in 1928<ref name="hilbert-ackermann1928">{{cite book |last1=Hilbert |first1=D. |last2=Ackermann |first2=W. |title=Grundzügen der theoretischen Logik |edition=1 |date=1928 |publisher=Verlag von Julius Springer |location=Berlin |page=4 |language=German}}</ref> (they also introduced <math>\rightleftarrows,\sim</math> while they use <math>\sim</math> as the main symbol in the whole book; <math>\leftrightarrow</math> is adopted by many followers such as Becker in 1933<ref name="becker1933">{{cite book |last1=Becker |first1=A. |title=Die Aristotelische Theorie der Möglichkeitsschlösse: Eine logisch-philologische Untersuchung der Kapitel 13-22 von Aristoteles' Analytica priora I |date=1933 |publisher=Junker und Dünnhaupt Verlag |location=Berlin |page=4 |language=German}}</ref>);
* <math>E</math> (prefix) in [[Jan Łukasiewicz|Łukasiewicz]] in 1929<ref name="lukasiewicz1929">{{cite book |last1=Łukasiewicz |first1=J. |editor1-last=Słupecki |editor1-first=J. |title=Elementy logiki matematycznej |orig-date=1929|date=1958 |publisher=Państwowe Wydawnictwo Naukowe |location=Warszawa |edition=2 |language=Polish}}</ref> and <math>Q</math> (prefix) in [[Jan Łukasiewicz|Łukasiewicz]] in 1951;<ref name="lukasiewicz1951">{{cite book |last1=Łukasiewicz |first1=J. |editor1-last=Słupecki |editor1-first=J. |title=Aristotle's Syllogistic from the Standpoint of Modern Formal Logic |orig-date=1951|date=1957 |publisher=Oxford University Press |location=Glasgow, New York, Toronto, Melbourne, Wellington, Bombay, Calcutta, Madras, Karachi, Lahore, Dacca, Cape Town, Salisbury, Nairobi, Ibadan, Accra, Kuala Lumpur and Hong Kong |edition=2 |language=Polish}}</ref> 
* <math>\supset\subset</math> in [[Arend Heyting|Heyting]] in 1930;<ref name="heyting1929">{{cite journal |last1=Heyting |first1=A. |title=Die formalen Regeln der intuitionistischen Logik |journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse |date=1930 |pages=42–56 |language=German}}</ref>
* <math>\Leftrightarrow</math> in [[Nicolas Bourbaki|Bourbaki]] in 1954;<ref name="bourbaki1954b">{{cite book |last1=Bourbaki |first1=N. |title=Théorie des ensembles |date=1954 |publisher=Hermann & Cie, Éditeurs |location=Paris |page=32 |language=French}}</ref>
* <math>\subset\supset</math> in Chazal in 1996;<ref name="chazal1996">{{cite book |last1=Chazal |first1=G. |title=Eléments de logique formelle |date=1996 |publisher=Hermes Science Publications |location=Paris}}</ref> 

and so on. Somebody else also use <math>\operatorname{EQ}</math> or <math>\operatorname{EQV}</math> occasionally.{{citation needed|date=September 2023}}{{vague|date=September 2023}}{{clarify|date=September 2023}}