IFF - meaning and definition. What is IFF
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What (who) is IFF - definition

LOGICAL CONNECTIVE
Material equivalence; Iff; ↔; ⇔; Bi-implication; All and only; Materially equivalent; Precisely when; Only if; If, and only if; If & only if; Just in case (catachresis); ⟺; If and Only If

IFF         
  • ''A'' is a proper subset of ''B''. A number is in ''A'' only if it is in ''B''; a number is in ''B'' if it is in ''A''.
  • ''C'' is a subset but not a proper subset of ''B''. A number is in ''B'' if and only if it is in ''C'', and a number is in ''C'' if and only if it is in ''B''.
WIKIMEDIA DISAMBIGUATION PAGE
Iff (disambiguation); IFF (disambiguation)
1. <file format> Interchange File Format. 2. Identify friend or foe (radar).
iff         
  • ''A'' is a proper subset of ''B''. A number is in ''A'' only if it is in ''B''; a number is in ''B'' if it is in ''A''.
  • ''C'' is a subset but not a proper subset of ''B''. A number is in ''B'' if and only if it is in ''C'', and a number is in ''C'' if and only if it is in ''B''.
WIKIMEDIA DISAMBIGUATION PAGE
Iff (disambiguation); IFF (disambiguation)
<mathematics, logic> if and only if, i.e. necessary and sufficient. For example, two figures are congruent iff one can be placed over the other so that they coincide. (2002-12-28)
iff         
  • ''A'' is a proper subset of ''B''. A number is in ''A'' only if it is in ''B''; a number is in ''B'' if it is in ''A''.
  • ''C'' is a subset but not a proper subset of ''B''. A number is in ''B'' if and only if it is in ''C'', and a number is in ''C'' if and only if it is in ''B''.
WIKIMEDIA DISAMBIGUATION PAGE
Iff (disambiguation); IFF (disambiguation)
¦ conjunction Logic & Mathematics if and only if.
Origin
1950s: arbitrary extension of if.

Wikipedia

If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false.

The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, P if and only if Q means that P is true whenever Q is true, and the only case in which P is true is if Q is also true, whereas in the case of P if Q, there could be other scenarios where P is true and Q is false.

In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. Some authors regard "iff" as unsuitable in formal writing; others consider it a "borderline case" and tolerate its use.

In logical formulae, logical symbols, such as {\displaystyle \leftrightarrow } and {\displaystyle \Leftrightarrow } , are used instead of these phrases; see § Notation below.

Examples of use of IFF
1. The IFF has been resisted by the Bush administration.
2. He added that plans were taking shape for a mini–IFF for immunisation, to be followed by the launch of a larger IFF to help double annual aid flows.
3. Eurostat said its ruling would not serve as a precedent for a bigger IFF.
4. "We know the American position on IFF," the spokesman told reporters.
5. Britain hopes to at least launch a pilot IFF to fund immunisation programmes.