29 lines
1.4 KiB
Markdown
29 lines
1.4 KiB
Markdown
---
|
||
title: Algebra of Logic
|
||
---
|
||
## Algebra of Logic
|
||
|
||
_Algebra of Logic_ or _Boolean algebra_ is a branch of mathematics. It deals with variables and their truth value. The variables have two possible states – `true` or `false`.
|
||
|
||
It was first introduced by George Boole in his book The Mathematical Analysis of Logic (1847).
|
||
|
||
Boolean algebra is fundamental to the development of digital electronics. It is responsible for making possible all modern computing.
|
||
|
||
The three basic operations in Boolean Algebra are `AND`, `OR`, and `NOT`. Consider two boolean variables `x` and `y`:
|
||
|
||
- `x AND y` is true if and only if both `x` and `y` are true
|
||
- `x OR y` is true if either of `x` or `y` are true
|
||
- `NOT x` is true if and only if `x` is false and vice versa
|
||
|
||
`NOT` of boolean statements can be refactored to apply directly to each variable. Consider the following :
|
||
- `NOT (x AND y) = NOT x OR NOT y`
|
||
- `NOT (x OR y) = NOT x AND NOT y`
|
||
|
||
The above statements are called "De Morgan's Laws." This is a very useful and important law in Boolean Algebra.
|
||
|
||
### More Information:
|
||
- Boolean algebra article: [Wikipedia](https://en.wikipedia.org/wiki/Boolean_algebra)
|
||
- The Calculus of Logic: [George Boole](https://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic.html)
|
||
- Boolean Algebra Demonstration: [Wolfram MathWorld](http://mathworld.wolfram.com/BooleanAlgebra.html)
|
||
- De Morgan's laws: [Wikipedia](https://en.wikipedia.org/wiki/De_Morgan%27s_laws)
|