Study Pure Mathematics notes on Groups and Binary Operations for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the ZIMSEC A-Level Pure Mathematics notes from 2020. It is a free notes for revision.
GLOBETROTTER EDUCATION MOVEMENT (C
2020 ONLINE SEMINAR PRESANTATION -15/05/20
Prepared by Tarakino N. P. (Trockers) - 0772978155/0717267175
GROUPS AND BINARY OPERATIONS
SYLLABUS (6042) OBJECTIVES
- define a binary operation
- define closure, commutation, association, distribution, identity and inverse element
- define a group
- use the basic properties to show that a given structure is, or is not, a group
- solve problems involving binary operations and properties of a group
Modular Arithmetic
- It is a form of arithmetic which deals with remainders/residues after integers are divided by a positive integer.
- Division of an integer by a positive integer produces a quotient and a remainder. These remainders will lead to modular arithmetic
Question
Find the value of $(21 \times 3) \bmod 4$.
Suggested Solution
\[
\begin{aligned}
(21 \times 3) \bmod 4 | =\frac{(21 \times 3)}{4} | =\frac{63}{4} | =15 \text { remainder } 3
\end{aligned}
\]
$\therefore(21 \times 3) \bmod 4=3$
BINARY OPERATION
- Binary operations on the set are calculations that combine two elements of the set (called operands) to produce another element of the same set.
- If G is a nonempty set, a binary operation $*$ on $G$ is a function $*$ :
Online Mathematics Seminar by Trockers and the Trotter...
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