In Exercises 29–34, find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}

Key Concepts

Sets

A set is a collection of distinct objects, considered as an object in its own right. In mathematics, sets are often defined by listing their elements within curly braces, such as {1, 2, 3}. Understanding sets is fundamental in algebra as they provide a way to group and analyze numbers or objects based on shared properties.

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, 3} and set B = {2, 3}, then the union A ∪ B = {1, 2, 3}. This concept is essential for combining data and understanding relationships between different groups.

Element Membership

Element membership refers to whether an object is a part of a set. This is denoted using the symbol '∈', meaning 'is an element of'. For instance, if we say 1 ∈ {1, 2, 3}, it indicates that 1 is a member of the set. Understanding element membership is crucial for determining the contents of sets and performing operations like union.