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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 : iI} is pairwise disjoint if for any i and j in I with ij,

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 : iI} of X such that {Ai} are pairwise disjoint and
Sets that are not the same.

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Related Questions

When was Disjointed Parallels created?

Disjointed Parallels was created in 1995.


What is a disjointed sentence?

the boy disjointed his arm when he fell off of his skateboard. ;p [: :}:


How can you make a sentence with the word disjointed?

"His logic seemed disjointed with the rest of his presentation."


How do you use the word disjointed in a sentence?

The enactment of the government policy was disjointed and uncoordinated from the very beginning. His disjointed speech left many listeners wondering what he actually meant to say.


What rhymes with disjointed?

Disappointed


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The cast of Disjointed Custody - 2012 includes: Britani Bateman as Mommy


What does modernism employ?

disjointed timelines


Solve -5(3n plus 4) 40.?

-5(3n plus 4) 40 is a set of disjointed expressions: it is not a formula and so cannot be solved.


What is a antonym for cohesive?

Framented or divided.


What is the definition of disjointed?

Lacking order or coherence.


Is disjointed a compound word?

Yes, "disjointed" is a compound word formed from the root word "joint." It means something that is disconnected, not properly aligned, or lacking coherence.


What is an example of a disjointed range designation in Excel?

A disjointed range in Excel consists of two or more separate ranges that are not contiguous. For example, if you want to select cells A1 to A5 and C1 to C5, you can specify this disjointed range as A1:A5, C1:C5 in a formula or function. This allows you to perform operations on non-adjacent cells simultaneously.