The following statements are logically equivalent:
Two or more sets are mutually disjoint if any two of the sets in question are disjoint. For example, {1,2,3}, {4,5,6}, and {7,8,9} are mutually disjoint. However, {1,2,3}, {4,5,6}, and {3,4} are not mutually disjoint, even though there is no number that belongs to all of them.
We can also say that a set U whose elements are themselves sets is mutually disjoint if its members are mutually disjoint. In symbols:
U is a partition of a set X if:
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