Question

the subset of partition is ce called cell
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Answer 1

Step-by-step explanation:

A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets[2] (i.e., X is a disjoint union of the subsets).

Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold:[3]

The family P does not contain the empty set (that is {\displaystyle \emptyset \notin P}\emptyset \notin P).

The union of the sets in P is equal to X (that is {\displaystyle \textstyle \bigcup _{A\in P}A=X}{\displaystyle \textstyle \bigcup _{A\in P}A=X}). The sets in P are said to cover X.

The intersection of any two distinct sets in P is empty (that is {\displaystyle (\forall A,B\in P)\;A\neq B\implies A\cap B=\emptyset }{\displaystyle (\forall A,B\in P)\;A\neq B\implies A\cap B=\emptyset }). The elements of P are said to be pairwise disjoint.

The sets in P are called the blocks, parts or cells of the partition.[4]

The rank of P is |X| − |P|, if X is finite.

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