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Boolean algebra
Posted by Kunal on March 18, 2024 at 5:31 pmWhat is the law of ‘Boolean algebra’? Explain with examples.
Nitesh replied 3 weeks, 3 days ago 2 Members · 1 Reply 
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Boolean algebra is a mathematical system that deals with variables that can only take on two possible values: true or false, often represented as 1 and 0, respectively. It is named after mathematician and logician George Boole, who developed the system in the mid19th century. Boolean algebra is widely used in computer science, digital electronics, and logic circuits.
The laws of Boolean algebra define a set of rules that govern the manipulation and simplification of logical expressions. These laws allow us to perform operations such as negation, conjunction (AND), disjunction (OR), and implication (IFTHEN) on Boolean variables. Here are some of the fundamental laws of Boolean algebra:

Identity Laws:
 Identity for OR: A + 0 = A
 Identity for AND: A â€¢ 1 = A
These laws state that if you OR a variable with 0, the result is the variable itself, and if you AND a variable with 1, the result is the variable itself.

Null Laws:
 Null for OR: A + 1 = 1
 Null for AND: A â€¢ 0 = 0
These laws state that if you OR a variable with 1, the result is 1, and if you AND a variable with 0, the result is 0.

Domination Laws:
 Domination for OR: A + A’ = 1
 Domination for AND: A â€¢ A’ = 0
These laws state that ORing a variable with its negation always results in 1, and ANDing a variable with its negation always results in 0.

Idempotent Laws:
 Idempotent for OR: A + A = A
 Idempotent for AND: A â€¢ A = A
These laws state that ORing or ANDing a variable with itself results in the variable itself.

Double Negation Law:
 Double Negation: A” = A
This law states that if you negate a variable twice, it is equivalent to the variable itself.
These are just a few examples of the laws of Boolean algebra. There are several other laws that govern more complex operations such as distributivity, De Morgan’s laws, and absorption. These laws provide a foundation for simplifying logical expressions and designing logical circuits in various fields.
