Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:05 minutes

Problem 85

Textbook Question

Let 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. M ∩ N

Verified step by step guidance

Identify the elements in set M: \{0, 2, 4, 6, 8\}.

Identify the elements in set N: \{1, 3, 5, 7, 9, 11, 13\}.

Determine the intersection of sets M and N, denoted as M \cap N, by finding common elements in both sets.

Since there are no common elements between sets M and N, the intersection is an empty set.

Conclude that sets M and N are disjoint because their intersection is an empty set.

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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 enclose elements. Understanding how to read and write sets is crucial for performing operations such as unions, intersections, and differences.

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 particularly relevant in the given question where we need to find M ∩ N. Knowing how to compute intersections helps in analyzing relationships between different sets.

Disjoint Sets

Disjoint sets are sets that have no elements in common, meaning their intersection is the empty set (A ∩ B = ∅). Identifying disjoint sets is important in various applications, such as probability and statistics, as it helps in understanding the relationships and overlaps between different groups. In the context of the question, recognizing disjoint sets aids in analyzing the provided sets M and N.