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What is a disjoint set?
ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.
What is disjoint?
A disjoint event is an event that can not happen at the same time
If A and B are disjoint and B and C are disjoint are A and C disjoint?
Not necessarily. For a counterexample, A and C could be the same set.
What is the domain for linear functions?
It can be anything that you choose it to be. It can be the whole real line or any proper subset - including disjoint subsets. It can be matrices, all of the same dimensions (Linear Algebra is based on them) or a whole host of other alternatives.
How do you determine subset of a single number?
A single number is not the same as a set containing a single number. A single number does not have any subsets.
What is disjointed set?
ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.
Can 2 disjoint sets be equal?
No, two disjoint sets cannot be equal. By definition, disjoint sets are sets that have no elements in common, meaning their intersection is empty. If two sets are equal, they contain exactly the same elements, which contradicts the notion of being disjoint. Therefore, if two sets are disjoint, they cannot be equal.
Can a number be rational and irrational the same time?
No, they are disjoint sets.
What is the difference between coplanar and non-coplanar vectors?
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Is direction is important for equal vectors?
Equal vectors are vectors having same direction of action or orientation as well as same magnitude. If two or more vectors have same magnitude but different direction then they cannot be called equal vectors. This shows that direction is important for equal vectors.
When are magnitudes of vectors added?
when the vectors have the same direction
What is the intersection of two disjoint sets?
Because they are disjoint, (ie. they contain none of the same elements) their intersection (what they both share in common) is the empty or null set.
