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

Verified step by step guidance

1. Identify the elements in the first set: \( \{1, 3, 5, 7\} \).
2. Identify the elements in the second set: \( \{2, 4, 6, 8, 10\} \).
3. Understand that the union of two sets includes all elements from both sets, without duplication.
4. Combine the elements from both sets into a single set, ensuring each element is unique.
5. List the elements of the union set in ascending order.

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.