   # 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 and B , if A ⊆ B then B e ⊆ A e ### 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 18ES
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 and B, if A ⊆ B then B e ⊆ A e

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:

Let A,B and C be any sets.

The objective is to prove that A×(BC)=(A×B)(A×C) for all sets A,B and C.

To show A×(BC)=(A×B)(A×C). It is enough to prove A×(BC)(A×B)(A×C) and (A×B)(A×C)A×(BC).

Show that A×(BC)(A×B)(A×C).

That is x, if xA×(BC), then x(A×B)(A×C).

Let x=(a,b)A×(BC).

By the definition of cross product aA and bBC.

By the definition of union, aA and [bB or bC].

This implies that [aA and bB] or [aA and bC].

By the definition of cross product, [(a,b)A×B] or [(a,b)A×C].

By the definition of union, (a,b)(A×B)(A×C).

Thus, fo all (a,b)A×(BC) then (a,b)(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
Evaluate 4sin(2x+2) when x is 6.

Trigonometry (MindTap Course List)

ReminderRound all answers to two decimal places unless otherwise indicated. Cancer Mortality RatesThe graph in ...

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

The 2000 Census showed that the town of Grandville had a population of 1020 residents. The 2010 Census was 1170...

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

Differentiate. 34. y=ecosx+cos(ex)

Single Variable Calculus

In Exercises 35-42, find functions f and g such that h = g f. (Note: The answer is not unique.) 39. h(x)=1x21

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

Expand each expression in Exercises 122. (y1y)(y+1y)

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

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