Question

List all the partitions of the set \(A=\\{a, b\\}\). Compare your answer to the answer to Exercise 5 of Section 11.3 .

Short answer

Accordingly, the partitions of the set \(A=\{a, b\}\) are \( \{\{a\}, \{b\}\} \) and \( \{\{a, b\}\} \).

Step-by-step solution

Understanding Set Partitions

A partition of a set 'A' is a set of nonempty subsets of 'A' such that every element 'a' from 'A' is in exactly one of these subsets. The subsets, in this case, are mutually exclusive, collectively exhaustive and non-empty. The partitions of a set consist of different ways these conditions can be fulfilled.

Partitioning the Set \(A=\{a, b\}\)

To find the partitions of set \(A=\{a, b\}\), one must first understand that there are exactly 2 elements. Therefore, considering the concept of partitions, the set \(A=\{a, b\}\) may have the following partitions: \n 1. \( \{\{a\}, \{b\}\} \) - Here, 'a' and 'b' are both individual subsets. \n 2. \(\{\{a, b\}\}\) - Here, 'a' and 'b' form a single subset.