   Chapter 6.4, 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
1 views

# In 4—10 assume that B is a Boolean algebra with operations + and•. Prove each statement using only the axioms for a Boolean algebra and statements proved in the text or in lower-numbered exercises. 4. Universal bound for 0: For every a in B, a ⋅ 0 = 0.

To determine

To Prove:

For all a in B,a0=0.

Explanation

Given information:

Let B be the Boolean algebra, with the operations, addition “ + ”and multiplication “

Concept used:

a¯+a=a+a¯     by the commutative law=1            by the complement law for 1

And

a¯a=aa¯     by the commutative law=0            by the complement law for 0

Calculation:

Assume that B is the Boolean algebra with the operations, addition“ + ”and multiplication“

Suppose a is any element of B.

Then, a¯ is the complement of a.

0=aa¯ By the Complement law for multiplication “

=(a1)a¯ By the Identity law for multiplication “

=(

### 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 