May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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7-4 Discrete Mathematical Structures
Examples
1. The set of natural numbers N is a semi-group with respect to addition.
2. The set of real numbers R is a semi-group with respect to addition.
3. The set of complex numbers C is a semi-group with respect to addition.
4. The set of square matrices of order n is a semi-group with respect to matrix multiplication.
5. The set of vectors is a semi-group with respect to vector addition.
6. The set of rational numbers Q is not a semi-group with respect to binary operation o defined
by a o b = a
2
+ b
2
.
7.3.2 Monoid
A monoid G is a system consisting of a non-empty set G of elements a, b, c,… and a binary
operation o satisfying the following postulates:
M1. The binary operation o is associative, that ...
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