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

검증된 단계별 안내

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.

List the elements of the first set: \(\{3, 0, 9, 6, 2\}\).

List the elements of the second set: \(\{2, 9, 0, 3, 6\}\).

Compare the elements of both sets to check if every element in the first set is also in the second set, and vice versa.

Conclude that since both sets contain the same elements, the statement that \(\{3, 0, 9, 6, 2\} = \{2, 9, 0, 3, 6\}\) is true.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.