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In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a man is a necessary condition for being a brother, but it is not sufficient—while being a man sibling is a necessary and sufficient condition for being a brother.
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.
However, only the occurrence of the necessary condition x may not always result in y also occurring. [2] In other words, when some factor is necessary to cause an effect, it is impossible to have the effect without the cause. [3] X would instead be a sufficient cause of y when the occurrence of x implies that y must then occur.
3. P is not necessary but it is sufficient: If (P OR Q) then S. We don't NEED P. We can get S from Q. But on the other hand if we DO have P, P is enough in itself to create S. No need for anything else. 4. P is not necessary AND not sufficient: If (P OR Q) AND R then S. P is not necessary. We can get S from Q even though we do not have P.
For example, but for running the red light, the collision would not have occurred.) The action is a necessary condition, but may not be a sufficient condition, for the resulting injury. A few circumstances exist where the but-for test is ineffective (see But-for test below).
An example of a necessary condition that is used for finding weak extrema is the Euler ... The Euler–Lagrange equation is a necessary, but not sufficient, ...
Consider lung cancer as an example. Smoking is a major component cause of lung cancer, but not everyone who smokes develops lung cancer. Other component causes might include genetic predisposition, other environmental factors, etc. Only when all necessary component causes are present does the sufficient cause of lung cancer come into play.
In other words, spontaneity is a necessary, but not sufficient, condition for a process to actually occur. Furthermore, spontaneity makes no implication as to the speed at which the spontaneous process may occur - just because a process is spontaneous does not mean it will happen quickly (or at all).