   # Use an element argument to prove each statement in 28-38. Assume that all sets are subsets of a universal set U. For all sest A , B , C, and D , if A ∩ C = ∅ then ( A × B ) ∩ ( C × D ) = ∅ ### 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 38ES
Textbook Problem
1 views

## Use an element argument to prove each statement in 28-38. Assume that all sets are subsets of a universal set U.For all sest A,B,C, and D, if   A ∩ C = ∅ then   ( A × B ) ∩ ( C × D ) = ∅

To determine

To Prove:

If AC=ϕ then (A×B)(C×D)=ϕ

### Explanation of Solution

Given information:

Let A,B and C be any sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

: Null set

Calculation:

The objective is to prove the result (A×B)(C×D)= is true for all A,B,C and D such that AC=.

Use the contradiction method to prove the result.

Let A,B,C and D be any sets such that AC=.

Suppose that (A×B)(C×D)=.

Let x(A×B)(C×D).

By the definition of intersection x(A×B) and x(C×D)

### 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
13-20 Solve the equation for x. sinx=0.3

Calculus (MindTap Course List)

A differential equation is separable if it can be written in the form: a) dydx=f(x)+g(y) b) dydx=f(g(x,y)) c) d...

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

Find f. f(x) = cos x, f(0) = 1, f(0) = 2, f(0) = 3

Single Variable Calculus: Early Transcendentals, Volume I

Evaluate the integral. 10. cos(1/x)x3dx

Calculus: Early Transcendentals

Expand each expression in Exercises 122. (x22x+1)2

Finite Mathematics and Applied Calculus (MindTap Course List)

A Function Given by a GraphThe following is the graph of a function f=f(x). Exercises S-1 through S-14 refer to...

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

Chip Sales The worldwide sales of flash memory chip (in billions of dollars) is approximated by S(t) = 4.3(t + ...

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