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

1:13 minutes

Problem 60

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. {0, 2} ⊆ D

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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 are represented by curly braces, and elements are listed within them. 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 its elements are also contained within another set. The notation 'A ⊆ B' indicates that set A is a subset of set B. To determine if a set is a subset, one must check if every element of the first set exists in the second set, which is essential for evaluating statements about set relationships.

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. Understanding the universal set helps in contextualizing other sets and determining the validity of subset relationships within the defined universe.