   # Let A = { a , b , c } , B = { b , c , d } , and C = { b , c , e } a. Find A ∪ ( B ∩ C ) , ( A ∪ B ) ∩ C , and ( A ∪ B ) ∩ ( A ∩ C ) . Which of these sets are equal? b. Find A ∩ ( B ∪ C ) , ( A ∩ B ) ∪ C , and ( A ∩ B ) ∪ ( A ∩ C ) . Which of these sets are equal? c. Find ( A − B ) − C and A − ( B − C ) . Are these sets equal? ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.1, Problem 16ES
Textbook Problem
1 views

## Let A = { a , b , c } , B = { b , c , d } , and C = { b , c , e } a. Find A ∪ ( B ∩ C ) , ( A ∪ B ) ∩ C , and ( A ∪ B ) ∩ ( A ∩ C ) . Which of these sets are equal? b. Find A ∩ ( B ∪ C ) , ( A ∩ B ) ∪ C , and ( A ∩ B ) ∪ ( A ∩ C ) . Which of these sets are equal?c. Find ( A − B ) − C and A − ( B − C ) . Are these sets equal?

To determine

(a)

Find A(BC), (AB)C and (AB)(AC), which of these sets are qual?

### Explanation of Solution

Given information:

A={a,b,c},B={b,c,d},and C={b,c,e}

Concept used:

: subset

: Intersection

:Union

Calculation:

The objective is to find the sets A(BC), (AB)C and (AB)(AC).

Find the set A(BC) as below,

A(BC)={a,b,c}({b,c,d}{b,c,e})={a,b,c}{b,c} by the definition of intersection={a,b,c}             by the definition of union.

Therefore, the set is A(BC)={a,b,c}.

Find the set (AB)C as below,

(AB)C=({a,b,c}{b,c,d}){b,c,e}={a,b,c,d}{b,c,e} by the definition of uion={b,c}             by the definition of intersection

Therefore, the set is (AB)C={b,c}

To determine

(b)

A(BC),(AB)C and (AB)(AC), which of these sets are equal?

To determine

(c)

Find (AB)C and A(BC) are these sets equal?

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Divide the following terms as indicated. 16a4b54ab3

Mathematics For Machine Technology

Reminder Round all answers to two decimal places unless otherwise indicated. Using Average Rate of Change The f...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Find the mean for the scores in the following frequency distribution table: X f 6 1 5 4 4 2 3 2 2 1

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

If f(x) = 5x, show that f(x+h)f(x)h=5x(5h1h)

Single Variable Calculus: Early Transcendentals

Explain why plagiarism is unethical.

Research Methods for the Behavioral Sciences (MindTap Course List)

Rising Median AGE Increased longevity and the aging of the baby boom generationthose born between 1946 and 1965...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

The x-coordinate of the center of mass of the region bounded by , x = 1, x = 2, y = 0 is: ln 2 1 2 ln 2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Solving Inequalities Solve the inequality. 82. x2ex 2ex 0

Precalculus: Mathematics for Calculus (Standalone Book)

Expand each expression in Exercises 122. (x+1)(x3)

Finite Mathematics and Applied Calculus (MindTap Course List)

The normal plane to at t = 1 has equation:

Study Guide for Stewart's Multivariable Calculus, 8th 