### Single Idea 9513

#### [catalogued under 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL]

Full Idea

We write 'P if and only if Q' as P↔Q. It is called the 'biconditional', often abbreviate in writing as 'iff'. It also says that P is both sufficient and necessary for Q, and may be written out in full as (P→Q)∧(Q→P).

Gist of Idea

We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P)

Source

E.J. Lemmon (Beginning Logic [1965], 1.4)

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.29

A Reaction

If this symbol is found in a sequence, the first move in a proof is to expand it to the full version.