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

1:24 minutes

Problem 52

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. C ⊆ U

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Key Concepts

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

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. In this context, understanding the relationships between different sets, such as subsets and unions, is crucial. A subset is defined as a set where all its elements are also contained in another set. This foundational concept is essential for analyzing the given statement about set C and set U.

Subset Notation

Subset notation is used to express the relationship between two sets, indicating that one set is entirely contained within another. The notation 'C ⊆ U' means that every element of set C is also an element of set U. Recognizing this notation helps in determining the truth of statements regarding set inclusion, which is central to solving the question.

Element Membership

Element membership refers to whether a specific element belongs to a set. To determine if C is a subset of U, one must check if each element of C (4, 10, 12) is present in U (2, 4, 6, 8, 10, 12, 14). Understanding this concept is vital for evaluating the truth of the subset relationship in the question.