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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 31
Chapter 1, Problem 31

Find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}

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Identify the two sets given: the first set is \(\{1,3,5,7\}\) and the second set is \(\{2,4,6,8,10\}\).
Recall that the union of two sets, denoted by \(\cup\), combines all elements from both sets without repeating any elements.
List all elements from the first set: \$1, 3, 5, 7$.
Add all elements from the second set: \$2, 4, 6, 8, 10$, making sure not to repeat any elements already listed.
Write the union set by combining all unique elements from both sets into one set.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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}.
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Set Notation

Set notation uses curly braces {} to list elements of a set. Elements are separated by commas, and each element is unique within the set. Understanding this notation helps in identifying and manipulating sets.
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Distinct Elements in Sets

When forming unions, repeated elements are only listed once. Recognizing that sets do not include duplicates ensures the union contains each element a single time, regardless of how many times it appears in the original sets.
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