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A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant.
The absence these conditions guarantees the outcome cannot occur, and no other condition can overcome the lack of this condition. Further, necessary conditions are not always sufficient. For example, AIDS necessitates HIV, but HIV does not always cause AIDS. In such instances, the condition demonstrates its necessity but lacks sufficiency.
[2] [3] For a concrete example, consider the conditional statement "if an object is a square, then it has four sides". It is a necessary condition that an object has four sides if it is true that it is a square; conversely, the object being a square is a sufficient condition for it to be true that an object has four sides. [4]
Business ethics operates on the premise, for example, that the ethical operation of a private business is possible—those who dispute that premise, such as libertarian socialists (who contend that "business ethics" is an oxymoron) do so by definition outside of the domain of business ethics proper.
A sine qua non (/ ˌ s aɪ n i k w eɪ ˈ n ɒ n, ˌ s ɪ n i k w ɑː ˈ n oʊ n /, [1] Latin: [ˈsɪnɛ kʷaː ˈnoːn]) or conditio sine qua non (plural: conditiones sine quibus non) is an indispensable and essential action, condition, or ingredient.
The commonly employed system S5 simply makes all modal truths necessary. For example, if p is possible, then it is "necessary" that p is possible. Also, if p is necessary, then it is necessary that p is necessary. Other systems of modal logic have been formulated, in part because S5 does not describe every kind of modality of interest.
If P and Q are "equivalent" statements, i.e. , it is possible to infer P under the condition Q. For example, the statements "It is August 13, so it is my birthday" and "It is my birthday, so it is August 13" are equivalent and both true consequences of the statement "August 13 is my birthday" (an abbreviated form of ).
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