Determine whether each statement is true or false. {3, 0, 9, 6, 2} = {2, 9, 0, 3, 6}

Key Concepts

Set Equality

Set equality states that two sets are considered equal if they contain exactly the same elements, regardless of the order in which those elements are listed. For example, the sets {1, 2, 3} and {3, 2, 1} are equal because they contain the same elements.

Element Uniqueness in Sets

In set theory, each element in a set is unique, meaning that duplicates are not counted. For instance, the set {1, 1, 2} is equivalent to the set {1, 2}, as the duplicate '1' is disregarded. This principle is crucial for determining set equality.

Order of Elements in Sets

The order of elements in a set does not affect its identity. This means that the arrangement of elements is irrelevant when comparing sets. For example, {a, b} is the same set as {b, a}, which is essential for evaluating the equality of two sets.