   Chapter 6.3, Problem 4ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

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

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
4 views

# For each of 1-4 find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U.For all sets A,B, and C, if B ∪ C ⊆ A then ( A − B ) ∩ ( A − C ) = ∅ .

To determine

For all sets A,B and C,if BCA then

(AB)(AC)=ϕ.

Explanation

Given information:

Let  A,B and C  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

For each find a counterexample to show that the statement ¡s false. Assume all sets are subsets of a universal set U.

Exercise

For all sets A,B and C,if BCA then

(AB)(AC)=ϕ.

Consider the statement as.

“For all sets A,B and C,if BCA then (AB)(AC)=ϕ ”.

The objective is to find a counter example to show that the above statement is false.

Consider that all sets are subsets of a universal set U.

Counterexample:

Let U be a universal set defined as,

U={1,2,3,4,5,6}.

Suppose for some sets A and B defined as,

A={1,4},B={1,2,3} and C={1,5,6}.

BC={1,2,3}{1,5,6}={1}A

### 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 