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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 Ref
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.
| 22435 | The logician's '→' does not mean the English if-then [Quine] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
| 9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |