78b8928b2c
* Adding "DeMorgans Law" I specified that the above statements were in fact demorgans laws. * spelling
30 lines
1.5 KiB
Markdown
30 lines
1.5 KiB
Markdown
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title: Algebra of Logic
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---
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## Algebra of Logic
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_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`.
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It was first introduced by George Boole in his book The Mathematical Analysis of Logic (1847).
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Boolean algebra is fundamental to the development of digital electronics. It is responsible for making possible all modern computing.
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The three basic operations in Boolean Algebra are `AND`, `OR`, and `NOT`. Consider two boolean variables `x` and `y`:
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- `x AND y` is true if and only if both `x` and `y` are true
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- `x OR y` is true if and only if either of `x`, `y` are true. If `x`, `y` are both true, `x OR y` is still true
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- `NOT x` is true if and only if `x` is false and vice versa
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`NOT` of boolean statements can be refactored to apply directly to each variable. Consider the following :
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- `NOT (x AND y) = NOT x OR NOT y`
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- `NOT (x OR y) = NOT x AND NOT y`
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The above statements are called "De Morgan's Laws." This is a very useful and important law in Boolean Algebra.
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### More Information:
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- The Calculus of Logic: <a href='http://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic.html' target='_blank' rel='nofollow'>George Boole</a>
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- Boolean algebra article: <a href='https://en.wikipedia.org/wiki/Boolean_algebra' target='_blank' rel='nofollow'>Wikipedia</a>
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- Boolean Algebra Demonstration: <a href='http://mathworld.wolfram.com/BooleanAlgebra.html' target='_blank' rel='nofollow'>Boolean Algebra</a>
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