## what is boolean algebra? and law Boolean algebra .(Boolean algebra Kay hai) : -

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**in this post, and will know in detail about its***what is boolean algebra (boolean algebra kay hai)***boolean algebra tutorial**. So let's start.
boolean algebra is a mathematical logic with only two values true and false.

boolean algebra is used to analyze and simplify digital circuits

**(boolean algebra simplification)**. It only uses binary numbers (0 and 1). Where 1 represents truth and 0 represents false.
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**What is boolean algebra in computer)**perform using boolean algebra to solve simple and complex operations**(boolean algebra solver).**
boolean algebra was discovered in 1854 by george boole.

boolean algebra is used to reduce the number of logic gates,

For example, suppose we have variable Y and presents whether it is raining outside or not.

- Truth, it's raining outside.
- Unreal, it is not raining outside.

More things happen in the real world like it is raining heavily outside, it is raining continuously, there is also sun with rain. But in boolean algebra there are only two things either it is raining or not happening. things get easier with boolean algebra

Read this post : - transformers type?

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__Boolean laws (Boolean rules): __

There are six types of boolean laws:- commutative law
- associative law
- AND
- OR
- inversiond
- istributive

**(rule of exchange) commutative law satisfies the following condition:**

__1).commutative law : -__
1) A.B = B.A

2) A + B = B + A

The law of exchange states that even if the order of the variable is changed, it cannot change the output of the logic circuit.

__2). associative law : -__
(A + B) + C = A + (B + C)

(A.B) .C = A. (B.C)

This rule states that the order of the input variable aligned will not affect its output.

__3). distributive law : -__distributive law satisfies the following condition.

A. (B + C) = A.B + A.C

__4). AND laws : -__
1) A.O = 0

2) A.1 = A

3) A.ANA

4) A.A = 0

__5). OR laws : -__
1) A + O = A

2) A + 1 = 1

3) A + A = A

__

4) A + A = 1

__

4) A + A = 1

__6). inversion law : -__This rule uses NOT operation. The inversion law means that the output of a double complement of a variable will itself be a variable,

=

A = A

__DE morgan's theorems (what DE Morgan therom?) : -__Its equation is as follows:

____ _ _

A + B = A . B

____ _ _

A + B = A . B

____ _ _

A. B = A + B

Its first equation shows that the NOR gate will be proportional to the bubbled AND gate.

The second equation shows that the NAND gate which is there will be proportional to the bubbled OR gate.

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__boolean algebra example : -__

**Boolean algebra question**

**Question: -**Create an input / output table for the following Boolean function?

**f(a1, a2, a3) = (a1.a2) + a3**

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