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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 and
Sets that are not the same.
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Difference betweenDisjoint sets and pairwise disjoint sets?
Assuming that, by 'disjoint', you mean that a collection of sets has an empty intersection, here is the difference between pairwise disjoint and 'disjoint': If a collection of sets is pairwise disjoint, it implies that the collection is 'disjoint': If no two sets overlap, then no k sets would overlap for any k, since this would require the overlap of at least two sets i.e. you know for sure that k things aren't in contact at a common point if you know that no two of them are in contact with each other. However, if a collection of sets is 'disjoint' (so the overall intersection is empty), it doesn't mean that the collection is pairwise disjoint. For instance, you could have a collection of 4 sets containing two overlapping pairs, where no set in one pair overlaps with a set in the other. So the intersection of the whole thing would be empty without pairwise disjointness. You could have a few things in contact with each other without all of them sharing a point of contact.
What is the graph of an arithmetic sequence whose first term is 1 and whose common difference is 0.5?
The graph will be a set of disjoint points with coordinates [n, 0.5*(1+n)]
What is a set that has no elements called?
An 'Empty Set' or a 'Nul Set'.
What are the kinds of sets?
set contains two kinds a negative and positive set
3p 4q36 10p 12q112 what is p and q?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared". There are no equations in the question - only a lot of disjoint expressions.
