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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1:23 minutes

Problem 23

Textbook Question

In Exercises 21–28, find the intersection of the sets. {s,e,t}∩{t,e,s}

Verified step by step guidance

Identify the elements in the first set: \( \{s, e, t\} \).

Identify the elements in the second set: \( \{t, e, s\} \).

Determine the common elements between the two sets.

List the elements that appear 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 {s, e, t}. The order of elements in a set does not matter, and duplicates are not allowed, meaning {s, e, t} is the same as {t, e, s}.

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, if we have sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection A ∩ B would be {2, 3}, 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, if we say 's ∈ {s, e, t}', it means that 's' is an element of the set. Understanding element membership is crucial for determining the intersection, as it helps identify which elements are shared between the sets.