Determine whether each statement is true or false. {2, 5, 8, 9} = {2, 5, 9, 8}

Verified step by step guidance

1. Identify the elements in each set. The first set is \{2, 5, 8, 9\} and the second set is \{2, 5, 9, 8\}.
2. Recall that in set theory, the order of elements in a set does not matter. Sets are defined by their elements, not the order of those elements.
3. Compare the elements of both sets. Check if both sets contain the same elements.
4. Verify that each element in the first set is present in the second set and vice versa.
5. Conclude that if both sets contain exactly the same elements, then the statement is true. Otherwise, it is false.>

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 set theory, each element in a set is unique, meaning that duplicates are not counted. For instance, the set {2, 2, 5} is equivalent to the set {2, 5} because the repeated element does not affect the overall composition of the set.

Order of Elements

The order of elements in a set does not matter. This means that the arrangement of elements does not influence the identity of the set. For example, the sets {a, b} and {b, a} are the same set, as they contain the same elements.