In Exercises 33–38, find the union of the sets. { a, e, i, o, u } ⋃ ∅

Key Concepts

Sets

A set is a well-defined collection of distinct objects, considered as an object in its own right. In this context, sets can contain elements such as numbers, letters, or other sets. The notation { a, e, i, o, u } represents a set of vowels, while ∅ denotes the empty set, which contains no elements.

Union of Sets

The union of two sets is a new set that contains all the elements from both sets, without duplication. It is denoted by the symbol '∪'. For example, if we take the union of { a, e, i, o, u } and ∅, the resulting set will include all the elements from the first set, as the empty set contributes no additional elements.

Empty Set

The empty set, denoted as ∅, is a unique set that contains no elements. It serves as the identity element for the union operation, meaning that the union of any set with the empty set will yield the original set. Understanding the role of the empty set is crucial when performing operations involving unions.