Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

1:05 minutes

Problem 7d

Textbook Question

Let U = {1, 2, 3, 4, 5} and A = {1, 2, 3}. Find A′.

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Key Concepts

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

Universal Set

The universal set, denoted as U, is the set that contains all possible elements relevant to a particular discussion or problem. In this case, U = {1, 2, 3, 4, 5} includes all elements under consideration, providing a context for defining subsets and their complements.

Subset

A subset is a set whose elements are all contained within another set. Here, A = {1, 2, 3} is a subset of the universal set U. Understanding subsets is crucial for operations involving set theory, such as finding complements.

Complement of a Set

The complement of a set A, denoted as A′, consists of all elements in the universal set U that are not in A. For the given sets, A′ would include the elements {4, 5}, which are in U but not in A. This concept is fundamental in set theory for distinguishing between included and excluded elements.