3.3. Partitions#

Self-Assessment:

The following questions can be used to check your understanding of the material covered in this chapter: $$

Suppose sets \(A\) and \(B\) are non-empty subsets of some sample space \(S\). If \(A\) and \(B\) are disjoint, which of the following are true?

Every element in \(S\) is either in \(A\) or \(B\)\(A \cap B = \emptyset\)\(A\) and \(B\) have no elements in common\(A \cup B = \emptyset\)

Which of these is true of a partition of a set \(S\)?

Every member of the set \(S\) must be in some subset of the partition.Elements may belong to more than one of the subsets in the partitionThe union of the subsets in the partition is equal to \(S\)The intersection of the subsets in the partition is equal to \(\emptyset\) No element in \(S\) may belong to more than one of the subsets in the partitionThe partition is a collection of subsets of \(S\)The intersection of the subsets in the partition is equal to \(S\)

Which of the following is an example of a partition of the set {1, 2, 3, 4}?

\(\{1, 2\}, \{2, 3\}, \{4\}\)\(\{1, 2\}, \{4\}, \)\(\{1\}, \{2\}, \{3\}, \{4\}\)\(\{1, 2\}, \{3\}, \{4\}\)

3.3.1. Terminology Review#

Use the flashcards below to help you review the terminology introduced in this section.

disjoint

Collections of data are disjoint if no data point belongs to more than one of the collections.

disjoint

Collections of data are disjoint if no data point belongs to more than one of the collections.

partition

A partition of a data set is a group of disjoint collections of data, such that every data point in the original data set belongs to exactly one of the collections.

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