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Boolean algebra is the algebra group in which the values of the variable are the values of truth, true and false, usually denoted as 1 and 0, respectively. It is used to study digital circuits and simplify them. It's often referred to as Binary or Rational Algebra. In the development of digital electronics, it has been fundamental and is provided for in all modern programming languages. It is often used in set theory and statistics.
- What are the Laws of Boolean Algebra?
- Weightage of Boolean Algebra in Class 11
- Illustrated Examples on Boolean Algebra
- FAQs on Boolean Algebra
What are the Laws of Boolean Algebra?
Conjunction (almost), disjunction (almost) and negation (almost) are the major operations performed in Boolean algebra. Therefore, this algebra is somewhat distinct from elementary algebra where computational and integer operations, such as addition, subtraction are the values of variables.
There are six types of Boolean algebra laws. They are:
1. Commutative law = A. B = B. A
A + B = B + A
2. Associative law = ( A. B ). C = A . ( B . C )
( A + B ) + C = A + ( B + C)
3. Distributive law = A. ( B + C) = (A. B) + (A. C)
A + (B. C) = (A + B) . ( A + C)
4. AND law = These laws use the AND operation. Therefore they are called AND laws.
5. OR law = These laws use the OR operation. Therefore they are called OR laws.
6. Inversion law = This law uses the NOT operation. The inversion law states that double inversion of variable results in the original variable itself.
Important Boolean Theorems
Here are a few Boolean theorems.
| Boolean Function |
Theorem Overview |
| Boolean Functions |
Boolean Functions and Expressions, K-Map and NAND Gates |
| Theorems of De Morgan |
De Morgan Theorem 1 and Theorem 2 |
Weightage of Boolean Algebra in Class 11
You will come across some of the Boolean algebra parts in the real number chapter, but it's not in much detail. The weightage of real numbers is 5-6 marks.
Illustrated Examples on Boolean Algebra
1. According to Boolean Algebra, (A+AB) =?
Solution.
It is equal to A.
2. Simplify the given expression: (A + B)(A + C)
Solution.
(A + B).(A + C)
A.A + A.C + A.B + B.C - Distributive law
A + A.C + A.B + B.C - Idempotent AND law (A.A = A)
A(1 + C) + A.B + B.C - Distributive law
A.1+ A.B + B.C - Identity OR law (1+ C =1)
A(1+B) + BC - Distributive law
A1+ BC - Identity OR law (1 + B =1)
A+(BC) - Identity AND law (A.1= A)
Answer: A+(BC)
3.State and verify Associative law.
Solution.
(A+B)+C=A+(B+C)
(A.B).C=A.(B.C)
(A+B)+C=A+(B+C)
Similarly, we can prove,
A.(B.C)=(A.B).C
FAQs on Boolean Algebra
Q: What are the Boolean algebra laws?
Q: In Boolean algebra, what is the absorption law?
Q: What is an example of Boolean algebra?
Q: Is Boolean algebra difficult?
Q: What are the 3 basic Boolean algebra operations?
Maths Algebra Exam
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