Definitions for if and only if
if and on·ly if

WiktionaryRate this definition:2.5 / 2 votes

1. if and only ifconjunction

   Is equivalent to; implies and is implied by; is true and false in the same cases as.

WikipediaRate this definition:0.0 / 0 votes

1. 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.

WikidataRate this definition:0.0 / 0 votes

1. If and only if

   In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements. In that it is biconditional, the connective can be likened to the standard material conditional combined with its reverse; 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. It is controversial whether the connective thus defined is properly rendered by the English "if and only if", with its pre-existing meaning. Of course, there is nothing to stop us stipulating that we may read this connective as "only if and if", although this may lead to confusion. In writing, phrases commonly used, with debatable propriety, as alternatives to P "if and only if" Q include Q is necessary and sufficient for P, P is equivalent to Q, P precisely if Q, P precisely when Q, P exactly in case Q, and P just in case Q. Many authors regard "iff" as unsuitable in formal writing; others use it freely. In logic formulae, logical symbols are used instead of these phrases; see the discussion of notation.

How to pronounce if and only if?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say if and only if in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of if and only if in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of if and only if in Pythagorean Numerology is: 7

Examples of if and only if in a Sentence

1. Maryanne Martini:

   We’ve run the numbers with polling and modeling in all 50 states, and our latest numbers show an independent could win outright in the Electoral College, and that they would draw votes equally from both sides, this is why we’re collecting signatures, recruiting volunteers, and laying the groundwork for an independent ticket IF, and ONLY IF, both parties put up unappealing candidates for the next presidential election.

2. Wolfgang Sobotka:

   There will be no wall, if and only if it is necessary will we introduce more controls (at Brenner) by slowing traffic and trains ... but circulation will be guaranteed.

3. RAS CARDO REGGAE:

   I wrote the book- to generations yet unborn- in trench town during my high school years as a prophecy of my reggae predictions. as a visionary, I saw what the jamaica today would become, if, and only if the status quo would help and respect the poor and disadvantaged people. jamaica and the world today does not surprise me. my reggae does not care if you are black or white just as long as you can make what is wrong- right! I am ras cardo, the creator.

4. Eyal Waldman:

   In China they prefer to use Chinese silicon and then after that non-U.S. silicon and only if they don't have that then U.S. silicon, so we are benefiting from that, we are seeing better growth in China.

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/If_and_Only_if
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/If_and_Only_if
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=if and only if