   Chapter 6.4, Problem 6ES ### 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
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# 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. 6. Uniquesness of 0: There is only one element of B that is an identity for +.

To determine

To Prove:

There is only one element of B that is an identity for +.

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:

Let B be the Boolean algebra, with the operations, addition "+" and multiplication "".

Suppose 0 and 0 are tile identity elements of B with respect to addition "+".

To show that there is only identity element of B with respect to addition "+" ¡t is enough to show that 0=0.

The Identity law for addition "+" tells that, for all aB.

a+0=a and a+0=a

It follows that,

a+0=a+0

Multiply both sides with a¯ ,

a¯(a+0

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