   # Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U. For all sets A , B , and C , if A ⊆ B and A ⊆ C then A ⊆ B ∩ C . ### 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 6.2, Problem 19ES
Textbook Problem
1 views

## Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U. For all sets A, B, and C, if A ⊆ B and A ⊆ C then A ⊆ B ∩ C .

To determine

To prove:

A×(BC)=(A×B)(A×C)

### Explanation of Solution

Given information:

Let A,B and C be any sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

The objective is to prove that for all sets A,B and C

A×(BC)=(A×B)(A×C).

To prove that A×(BC)=(A×B)(A×C), prove that

A×(BC)(A×B)(A×C)

(A×B)(A×C)A×(BC).

Prove that A×(BC)(A×B)(A×C).

Suppose (x,y)A×(BC).

Then xA and yBC.

By definition of intersection xB and yC.

As xA and yB,(x,y)A×B.

Also, xA and yC,(x,y)A×C

By definition of intersection, since (x,y)A×B and (x,y)A×C.

(x,y)(A×B)(A×C)

Therefore, A×(BC)(A×B)(A×C)

### 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
In problems 24-26, find the intercepts and graph. 25.

Mathematical Applications for the Management, Life, and Social Sciences

Find the mean, median, and mode for the following sample of scores: 4, 5, 2, 7, 1, 3, 5

Statistics for The Behavioral Sciences (MindTap Course List)

The appropriate option for the value of the indefinite integral ∫sinx2 dx.

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

In Exercises 2124, factor each expression completely. 24. 12tt 6t2 18t

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

A parameterization of the curve at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th

Reminder Round all answer to two decimal places unless otherwise indicated. Difference Quotients Calculate the ...

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

Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics and Applied Calculus (MindTap Course List) 