May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Boolean Algebra 9-5
(4) Identity Laws
0 + 1 = 1 + 0 = max{1, 0} = 1
and 0.1 = 1.0 = min{1, 0} = 0
Hence, 0 is identity for addition and 1 is identity for multiplication.
(5) Complement Laws
1 1 1 max 1 1 i e 1
11 1 mi
+′=+=
{}
=+′=
′= =
00
0
,..
..
xx
nn1 ie
for
,...00 0
{}
=′=
∈
xx
xB
Thus, {B, +, ., ′} is a Boolean algebra.
Note 9.2 As the design and analysis of electronic devices is based on two-element Boolean
algebra, we shall confine our discussion to {B, +, ., ′, 0, 1}.
9.2.1 Boolean Variables
Boolean variables are denoted by x, y, z,… or x
1
, x
2
, x
3
,…, x
n
and can assume values 0 and 1.
9.2.2 Boolean Expression
Boolean expressions are made up of Boolean Variables and Boolean operators. For example,
x + y, xy, x + y + z, x + (
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