Binary Operation Table
A binary operation table, also known as a Cayley table or operation table, is a systematic way to display the results of applying a binary operation to elements of a set.
In this table, each row represents one of the elements of the set, and each column represents another element. The cell at the intersection of a row and a column contains the result of applying the binary operation to the corresponding pair of elements.
For example, let’s consider a set A={0, 1, 2, 3} with addition modulo(⊕) as operation.
⊕ | 1 | 2 | 3 | 4 |
---|---|---|---|---|
1 | 2 | 3 | 4 | 1 |
2 | 3 | 4 | 1 | 2 |
3 | 4 | 1 | 2 | 3 |
4 | 1 | 2 | 3 | 4 |
Binary Operation
Binary Operation is an operation defined for any set S such that it takes two elements from S as input and produces a single element in S as output. As the name suggests, binary operations require at least two inputs as it is defined from the cartesian product of set to set itself.
In this article, we will explore binary operations, binary operations definition, properties of binary operations, types of binary operations, and many more. We will also discuss the applications of binary operations and solve some binary operation examples. Let’s start our learning on the topic “Binary Operation”.
Table of Content
- What are Binary Operations?
- Properties of Binary Operations
- Types of Binary Operations
- Binary Operation Table
- Applications of Binary Operations
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