Find the union of the sets. {e,m,p,t,y} ∪ ∅

검증된 단계별 안내

Identify the two sets involved in the union operation: the first set is \(\{e, m, p, t, y\}\) and the second set is the empty set \(\emptyset\).

Recall the definition of union of two sets: the union \(A \cup B\) is the set containing all elements that are in \(A\), or in \(B\), or in both.

Since the second set is the empty set \(\emptyset\), it contains no elements to add to the union.

Therefore, the union \(\{e, m, p, t, y\} \cup \emptyset\) will contain exactly the elements of the first set.

Write the union result as \(\{e, m, p, t, y\}\), which is the same as the first set.

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주요 개념

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

Set Union

The union of two sets combines all unique elements from both sets into one set. It is denoted by the symbol ∪. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.

Empty Set (∅)

The empty set, denoted by ∅, is a set that contains no elements. It is a subset of every set, and when combined with another set using union, it does not add any new elements.

Properties of Set Operations

Set operations follow specific properties such as identity and idempotent laws. For union, the identity property states that the union of any set with the empty set is the set itself, meaning A ∪ ∅ = A.