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  • logic - What is the difference between necessary and sufficient . . .
    But as we see in the table Q can be true also when P is false (the third line in the table) So P is "just" a sufficient condition for Q Q is a necessary condition for P It is obvious from the table P can be true "only" when Q is true (the first line in the table) Note that we do not consider the second line About $\lnot A \implies \lnot B$
  • logic - sufficient condition vs necessary condition - Mathematics Stack . . .
    A proposition is a sufficient or necessary condition for another proposition, not in and of itself So, saying "the first sentence is (or is not) a necessary condition" is meaningless, without saying for what it is (or it not) a necessary condition The same for sufficient condition
  • What is the difference between necessary condition sufficient condition?
    Getting good grades is a necessary condition to get accepted into a prestigious university Solving the Riemann hypothesis is sufficient to get accepted into a prestigious university So in short, a sufficient condition guarantees the occurrence of another condition But a necessary condition doesn't guarantee it
  • logic - Necessary and sufficient condition meaning - Mathematics Stack . . .
    Here rain is sufficient condition for road to be wet, but not the necessary condition , because road could be wet by any other operation , i e throwing water buckets on it Similarly consider a statement
  • optimization - Optimality conditions - necessary vs sufficient . . .
    A condition is sufficient if that condition being true is enough to conclude that some other condition is true as well In this case, if a site with gradient $0$ has a positive semi-definite Hessian, it has to be a minimum The necessary gradient condition is weakened by the fact that a site with gradient $0$ could also be a saddle point
  • logic - about necessary and sufficient condition, again - Mathematics . . .
    The phrase "A is a necessary sufficient condition" has no meaning without reference to a second condition As for an example, being a square is a sufficiently strong condition to guarantee being a rectangle On the other hand, it is absolutely necessary to be a rectangle if you have any hope of being a square
  • Difference between necessary and necessary but not sufficient?
    The statement that the condition is necessary is an implication in one direction, and the statement that this condition is not sufficient is the negation of the implication in the other direction Thus, we have the structure (safe $\to$ conditions) $\land \neg$ (conditions $\to$ safe)
  • The meaning of the sufficient condition - Mathematics Stack Exchange
    In the language of sufficiency, we would say that "A sufficient condition for a vector field's curl to be zero is that it is conservative " The order is important there, as the converse, "If a field has zero curl, then it is conservative," is false (see for example this answer: Does zero curl imply a conservative field?


















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