Sentence examples for sufficient or necessary from inspiring English sources

While there have been some reforms, mandatory minimum sentences often cause the imprisonment of offenders for far longer than is sufficient or necessary.

The question now is whether the presence of such an atom (usually carbon) is either sufficient or necessary for the molecule to be chiral.

Furthermore, more effective sufficient or necessary conditions for the observability of SBCNs are obtained directly from weighted pair graphs.

Apart from the questions of whether operational definitions are sufficient or necessary, it is actually unclear what types of things operations are, and how they should be specified.

Consistency can be used to evaluate whether a particular condition or the combinations of conditions can be regarded as a sufficient or necessary condition of the result.

He and more recent writers have posed simple counterexamples to these being even sufficient or necessary conditions for pleasure, using perceptual examples such as Aristotle used in expounding his theory.

Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations.

Thus, in the following two sections we will focus on the existence and non-existence of order-2 limit cycles for model (2.2) and provide some sufficient conditions or necessary conditions on this topic.

Since the advent of modernism, beauty had been questioned as a sufficient, or even necessary, requirement for art.

It was no longer sufficient, or even necessary, for an arts leader to know anything about the arts he or she was supposedly managing.

However, neither any of these properties alone nor all of them together are sufficient or even necessary for a complete description of glass.