   Chapter 6.3, Problem 14ES ### 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
1 views

# For each of 5-21 prove each statement that I true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.For all sets A,B, and C, if A ∩ C = B ∩ C and A ∪ C = B ∪ C , then A=B.

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A,Band C

ifACBC and ACBC then AB.

Explanation

Given information:

Let  A,B and C  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Consider the statement,

If ACBC and ACBC.

The objective is to verify whether the statement is true or not.

Recall, the definition for union, and intersection,

Suppose A and B are two subsets of a universal set .

1. The union of A and B is denoted by AB, and is defined by,
2. AB={xU|xA, or, xB}

3. The intersection of A and B is denoted by AB, and is defined by
4. AB={xU|xA, and, xB}.

Let A,B and C is any sets.

Suppose that if xA when xC or xC.

Case 1.

For xA and xC

### 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 