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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0:59 minutes

Problem 34

Textbook Question

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

Verified step by step guidance

Identify the two sets involved in the union operation: Set A = \{e, m, p, t, y\} and Set B = \emptyset (the empty set).

Recall the definition of the union of two sets: The union of two sets A and B, denoted as A \cup B, is the set of elements that are in A, in B, or in both.

Consider the properties of the empty set: The empty set, \emptyset, contains no elements.

Apply the union operation: Since the empty set has no elements, the union of any set with the empty set is simply the original set.

Conclude that the union of \{e, m, p, t, y\} and \emptyset is \{e, m, p, t, y\}.

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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. 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.