Biconditional, also called material equivalence, is a logical connective that means ” if and only if “.

Not to be confused with equivalence relation and logical equivalence

Biconditional has the following truth table:

TTT
TFF
FTF
FFT
Alternative symbols of biconditional include (\iff in latex) and (\equiv in latex). Though those symbols are also used to express [[./logical equivalencelogical equivalence]]. The meaning of symbols depend on context. The phrase “if and only if” or “iff” is also often used.

Relationship with Logical Equivalence

See: logical equivalence

Biconditional and logical equivalence has close relation, but they are not the same. When and are logical equivalent, the biconditional is always true (a tautology).