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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1:21 minutes

Problem 21

Textbook Question

In Exercises 21–28, find the intersection of the sets. {1,2,3,4}∩{2,4,5}

Verified step by step guidance

Identify the elements in the first set: \( \{1, 2, 3, 4\} \).

Identify the elements in the second set: \( \{2, 4, 5\} \).

Determine which elements are common to both sets.

List the common elements found in both sets.

The intersection of the sets is the set of these common elements.

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Key Concepts

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

Sets

A set is a collection of distinct objects, considered as an object in its own right. In mathematics, sets are often defined by listing their elements within curly braces, such as {1, 2, 3, 4}. Understanding sets is fundamental for operations like union, intersection, and difference, which are key to set theory.

Intersection of Sets

The intersection of two sets is a new set that contains all the elements that are common to both sets. It is denoted by the symbol '∩'. For example, the intersection of {1, 2, 3, 4} and {2, 4, 5} is {2, 4}, as these are the elements present in both sets.

Element Membership

Element membership refers to whether an object is a member of a set. This is often denoted using the symbol '∈'. For instance, in the set {1, 2, 3, 4}, the number 2 is an element, so we can say 2 ∈ {1, 2, 3, 4}. Understanding element membership is crucial for determining intersections and other set operations.