Determine whether each statement is true or false. {2, 5, 8, 9} = {2, 5, 9, 8}
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<insert step 1> Identify the elements in each set. The first set is \{2, 5, 8, 9\} and the second set is \{2, 5, 9, 8\}.
<insert step 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.
<insert step 3> Compare the elements of both sets. Check if both sets contain the same elements.
<insert step 4> Verify that each element in the first set is present in the second set and vice versa.
<insert step 5> Conclude that if both sets contain exactly the same elements, then the statement is true. Otherwise, it is false.>
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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.
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.