What is the origin of 'sleep tight'?

Read moreOne of the mysteries of the English language finally explained.

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Used to introduce a condition which is necessary as well as sufficient.

*‘witches are real if and only if there are criteria for identifying witches’*-
*‘I realized it's OK to make mistakes if and only if you take them and turn them around to be positive situations.’* -
*‘The ganja addict who suffers from a mental breakdown, which is controlled by medication, if and only if the medication is taken.’* -
*‘Preferences over probability gambles are rational, that is, satisfy the substitution and continuity conditions, if and only if they have the expected utility property.’* -
*‘Which is good, since I plan to further my studies, if and only if possible.’* -
*‘We showed that in the absence of phase information, genotyping errors can be detected if and only if there is Mendelian inconsistency at one or more of the markers.’* -
*‘The venue is not very far from Shanghai downtown - if and only if you have a car.’* -
*‘The problem is the formal definition of the logical constructs of if and only if, or sufficient and necessary conditions.’* -
*‘They will come to our defence if and only if it is in their national interests to do so, regardless of what we've done for them.’* -
*‘Note that it terminates with a random allocation that satisfies quota if and only if there exists an allocation that both satisfies quota and obeys the lower bound.’* -
*‘But this will happen if and only if we educate our labour pool properly and prepare them for a brave new world outside of making beds and cleaning hotel rooms.’*

View synonyms**on condition that**, provided, provided that, providing, providing that, presuming, presuming that, supposing, supposing that, assuming, assuming that, on the assumption that, allowing, allowing that, as long as, given that, with the provision that, with the proviso that, on the understanding that, with the understanding that, if and only if, contingent on, in the event that-