Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 27

Chapter 1, Problem 27

Concept Check Let A = {1, 2, 3, 4, 5, 6}, B = {1, 3, 5,}, C = {1, 6}, and D = {4}. Find each set. a. A ∩ D b. B ∩ C c. B ∩ A d. C ∩ A

Verified step by step guidance

Recall that the intersection of two sets, denoted by \(A \cap B\), is the set of all elements that are common to both sets \(A\) and \(B\).

For part (a), find \(A \cap D\) by identifying elements that are in both \(A = \{1, 2, 3, 4, 5, 6\}\) and \(D = \{4\}\).

For part (b), find \(B \cap C\) by identifying elements common to \(B = \{1, 3, 5\}\) and \(C = \{1, 6\}\).

For part (c), find \(B \cap A\) by identifying elements common to \(B = \{1, 3, 5\}\) and \(A = \{1, 2, 3, 4, 5, 6\}\). Note that since \(B\) is a subset of \(A\), this intersection will be \(B\) itself.

For part (d), find \(C \cap A\) by identifying elements common to \(C = \{1, 6\}\) and \(A = \{1, 2, 3, 4, 5, 6\}\). Since \(C\) is a subset of \(A\), this intersection will be \(C\) itself.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Set Intersection

The intersection of two sets includes all elements that are common to both sets. It is denoted by the symbol '∩'. For example, if Set A = {1, 2, 3} and Set B = {2, 3, 4}, then A ∩ B = {2, 3}.

Set Notation and Elements

Sets are collections of distinct elements, usually enclosed in curly braces {}. Understanding how to read and interpret these elements is essential for performing operations like union, intersection, and difference.

Basic Set Operations

Besides intersection, basic set operations include union (combining elements from both sets) and difference (elements in one set but not the other). Knowing these helps in manipulating and understanding relationships between sets.

Recommended video:

04:12

Algebraic Operations on Vectors

Related Practice

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

648

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = ½ x - 2

530

views

Textbook Question

Concept Check Graph the points on a coordinate system and identify the quadrant or axis for each point. (4.5, 7)

644

views

Textbook Question

Write each rational expression in lowest terms. See Example 2. (m² - 4m + 4) / (m² + m - 6)

770

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.