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Boolean algebra
What is the law of ‘Boolean algebra’? Explain with examples.
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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 mid-19th 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 (IF-THEN) on Boolean variables. Here are some of the fundamental laws of Boolean algebra:
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Identity Laws:
- Identity for OR: A + 0 = A
- Identity for AND: A • 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.
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Null Laws:
- Null for OR: A + 1 = 1
- Null for AND: A • 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.
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Domination Laws:
- Domination for OR: A + A’ = 1
- Domination for AND: A • 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.
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Idempotent Laws:
- Idempotent for OR: A + A = A
- Idempotent for AND: A • A = A
These laws state that ORing or ANDing a variable with itself results in the variable itself.
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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.
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