Sentence examples for mutually disjoint sets from inspiring English sources
Considering a context model containing more than one context property, we require that such context properties feature mutually disjoint sets of context events, so that evolutions of different context properties within the same context do not correlate explicitly.
To make it possible, the execution domain Σ F is built as asynchronous product of fragments F +. We assume that fragments within a single context-aware system have uncorrelated actions, i.e., such fragments have mutually disjoint sets of actions.
Now the impossible proposition that A ∧ ¬A just is the inconsistent set {{w1, w2}, {w3, w4, w5}}, whereas the impossible proposition that B ∧ ¬B just is the inconsistent set {{w2, w3, w4}, {w1, w5}}; and these are distinct inconsistent sets of sets of worlds (they are sets of mutually disjoint sets of genuine worlds).
> -wrap-foot> Cometricstrics for comparing the clusterings [Jaccard Index (Jaccard, 1901); Variation of Information metric (Meila, 2007)] assume that a clustering is a partitioning of a dataset into mutually disjoint sets.
Now suppose \(A\) to be partitioned into a (necessarily infinite) mutually disjoint set \(P\) of pairs.
An interpretation I of L* consists again of two mutually disjoint nonempty sets: the set of possible worlds and the set of haecceities.
SOCEiCP is regarded as one of the most difficult problems to solve, because the Lorentz spectrum may be the union of finitely many mutually disjoint connected sets and each connected set is either a singleton or a closed interval of positive length (not finite and not countable) [12].
Suppose that a given set of cycles has mutually disjoint species sets, but the orders of the cycles sum to less than k.
Refering back to Figure 5, two mutually disjoint cover sets with covers in total do exist.
Let us call Zermelo's 1908 formulation the combinatorial axiom of choice: CAC: Any collection of mutually disjoint nonempty sets has a transversal.
Then, Lemma 1 can be applied to and individually to form two corresponding mutually disjoint cover sets, denoted as and, with covers and covers, respectively.
