In Exercises 29–34, find the union of the sets. {e,m,p,t,y} ∪ ∅

Key Concepts

Sets

A set is a collection of distinct objects, considered as an object in its own right. Sets are typically denoted by curly braces, and the elements within a set can be anything, such as numbers, letters, or other sets. Understanding the basic properties of sets, including how to define and manipulate them, is essential for solving problems involving unions, intersections, and differences.

Union of Sets

The union of two sets is a new set that contains all the elements from both sets, without duplicates. It is denoted by the symbol '∪'. For example, if set A = {1, 2} and set B = {2, 3}, then the union A ∪ B = {1, 2, 3}. This concept is crucial for combining sets and understanding how they interact.

Empty Set

The empty set, denoted by '∅', is a set that contains no elements. It is a fundamental concept in set theory, serving as the identity element for the union operation. When any set is united with the empty set, the result is the original set itself, which is important for understanding how unions work in various scenarios.