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

1:15 minutes

Problem 51b

Textbook Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. A ⊆ U

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Key Concepts

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

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, sets A, B, C, D, and U are defined with specific elements. Understanding how to read and interpret set notation is crucial for determining relationships between sets, such as subsets and intersections.

Subset

A subset is a set where all elements are contained within another set. The notation A ⊆ U indicates that set A is a subset of set U, meaning every element in A must also be an element of U. Recognizing subsets is essential for evaluating statements about set relationships, such as the one presented in the question.

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 includes all elements from the sets A, B, C, and D, as well as additional elements. Understanding the concept of a universal set helps in determining whether other sets are subsets of it.