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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0:50 minutes

Problem 27

Textbook Question

In Exercises 21–28, find the intersection of the sets. {a,b,c,d}∩∅

Verified step by step guidance

Identify the sets involved in the intersection: Set A = \{a, b, c, d\} and Set B = \emptyset (the empty set).

Recall that the intersection of two sets, denoted as A \cap B, is the set containing all elements that are common to both sets.

Understand that the empty set, \emptyset, contains no elements.

Since the empty set has no elements, there are no elements that can be common between Set A and the empty set.

Conclude that the intersection of any set with the empty set is always the empty set, \emptyset.

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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. Sets are typically denoted by curly braces, such as {a, b, c, d}. Each element in a set is unique, and the order of elements does not matter. Understanding sets is fundamental in mathematics, particularly in topics like set theory, probability, and algebra.

Intersection of Sets

The intersection of two sets is a new set that contains all elements that are common to both sets. It is denoted by the symbol '∩'. For example, if we have sets A = {a, b, c} and B = {b, c, d}, then A ∩ B = {b, c}. The intersection is crucial for understanding relationships between sets and is often used in various mathematical applications.

Empty Set

The empty set, denoted by ∅, is a set that contains no elements. It is a fundamental concept in set theory, representing the idea of 'nothing' or 'no items'. When finding the intersection of any set with the empty set, the result is always the empty set, as there are no common elements. This concept is essential for understanding the properties of sets and their interactions.