Iff

https://arbital.com/p/iff

by Alexei Andreev Jun 11 2016 updated Oct 4 2016

If and only if...


Iff is a shorthand for "if and only if". Its logical symbol is $~$\leftrightarrow$~$.

"A iff B" ($~$A \leftrightarrow B$~$) is quite distinct from "if A then B" ($~$A \rightarrow B$~$). Consider the stipulation "If the dog barks, then it will soon bite". This would not obligate the dog to bark a warning before biting. The "if" relation isn't symmetrical. As such, the dog might sometimes bite spontaneously, with no barking at all.

If we wanted to ensure that biting is always forewarned by barking, we would instead stipulate "Iff dog barks, then it will soon bite". This is equivalent to

With "iff", the implication runs in both directions.