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

Verified step by step guidance

1. Understand that the problem is asking whether the two sets \(\{2, 5, 8, 9\}\) and \(\{2, 5, 9, 8\}\) are equal.
2. Recall the definition of set equality: Two sets are equal if and only if they contain exactly the same elements, regardless of the order.
3. List the elements of the first set: \$2, 5, 8, 9$.
4. List the elements of the second set: \$2, 5, 9, 8$.
5. Compare the elements of both sets to confirm that they contain the same elements, just in a different order, which means the sets are equal.

Key Concepts

Set Equality

Two sets are equal if and only if they contain exactly the same elements, regardless of the order or repetition. This means that every element of the first set must be in the second set, and vice versa.

Order Irrelevance in Sets

In set theory, the order of elements does not matter. For example, {2, 5, 8} is the same set as {5, 8, 2} because they contain the same elements, just arranged differently.

Element Membership

Element membership refers to whether a particular item is contained within a set. To verify set equality, you check that each element of one set is a member of the other set.