Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:44 minutes

Problem 31

Textbook Question

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

Verified step by step guidance

Step 1: Understand the concept of union in set theory. The union of two sets combines all unique elements from both sets into a single set. Duplicate elements are not repeated in the union.

Step 2: Identify the elements in the first set, which are {1, 3, 5, 7}. These are the odd numbers from 1 to 7.

Step 3: Identify the elements in the second set, which are {2, 4, 6, 8, 10}. These are the even numbers from 2 to 10.

Step 4: Combine all elements from both sets into a single set, ensuring no duplicates. The union will include all odd numbers from the first set and all even numbers from the second set.

Step 5: Write the union set in ascending order for clarity. This ensures the final set is organized and easy to interpret.

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Key Concepts

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

Sets

A set is a collection of distinct objects, considered as an object in its own right. In mathematics, sets are often denoted by curly braces, such as {1, 2, 3}. Each element in a set is unique, meaning that no duplicates are allowed. Understanding sets is fundamental for operations like union, intersection, and difference.

Union of Sets

The union of two sets is a new set that contains all the elements from both sets, without any 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 from different sources in mathematics.

Element Membership

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