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
1:46 minutes
Problem 92
Textbook Question
Textbook QuestionLet U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. Q ∩ R′
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sets and Set Notation
A set is a collection of distinct objects, considered as an object in its own right. Set notation is used to define and describe these collections, using symbols like braces {} to denote the elements. Understanding how to read and write sets is crucial for performing operations such as unions, intersections, and complements.
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Intersection of Sets
The intersection of two sets, denoted as A ∩ B, is the set of elements that are common to both A and B. This concept is essential for determining shared elements between sets, which is a key operation in set theory. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.
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Parallel & Perpendicular Lines
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. This concept helps in understanding the relationship between a set and the universal set, allowing for operations that involve elements outside of a given set. For instance, if U = {0, 1, 2, 3, 4} and A = {1, 2}, then A′ = {0, 3, 4}.
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