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

Verified step by step guidance

1. Understand that two sets are equal if and only if they contain exactly the same elements, regardless of the order in which the elements are listed.
2. List the elements of the first set: \(\{3, 0, 9, 6, 2\}\).
3. List the elements of the second set: \(\{2, 9, 0, 3, 6\}\).
4. Compare the elements of both sets to check if every element in the first set is also in the second set, and vice versa.
5. Conclude that since both sets contain the same elements, the statement that \(\{3, 0, 9, 6, 2\} = \{2, 9, 0, 3, 6\}\) is true.

Key Concepts

Set Equality

Two sets are equal if and only if they contain exactly the same elements, regardless of order or repetition. This means 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, {1, 2, 3} is the same set as {3, 2, 1}, because sets are unordered collections.

Element Uniqueness in Sets

Sets do not consider repeated elements; each element is unique within a set. For instance, {1, 1, 2} is equivalent to {1, 2} because duplicates are ignored.