Definitions for if and only if
This page provides all possible meanings and translations of the word if and only if
if and only if(Conjunction)
Is equivalent to; implies and is implied by; is true and false in the same cases as.
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.
Sample Sentences & Example Usage
A country is not developed by constructing bridges, houses or roads but it is developed only if the brains of the people living in that country are developed, only if their level of culture is raised and only if an infinite importance is given to the science and to the knowledge!
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"if and only if." Definitions.net. STANDS4 LLC, 2016. Web. 13 Feb. 2016. <http://www.definitions.net/definition/if and only if>.