if and only if

if and only if

A way of writing two conditionals at once: both a conditional and its converse.

For example, the statement "A triangle is equilateral iff its angles all measure 60°" means both "If a triangle is equilateral then its angles all measure 60°" and "If all the angles of a triangle measure 60° then the triangle is equilateral".

Biconditionals can be written using the ⇔ symbol:

A triangle is equilateral ⇔ its angles all measure 60°


See also

Inverse, contrapositive

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