Boolean Algebra - Introduction
Introduction The algebra of logic, which deals with the study of binary variables and logical operations, and also manipulates them is known as Boolean Algebra. This makes it possible to tr...
Laws of Boolean Algebra
# Boolean Postulates
According to Boolean Postulates of Boolean Algebra,
| OR law | AND law | NOT law |
| A + 0 = A | A.1 = A | 0' = 1 |
| A + 1 = 1 | A.0 = 0 | 1' = 0 |
| A + A= A | A.A = A | A'' = A |
| A + A' = 1 | A.A' = 0 |
# Duality Principle
It states that, "dual expression of a Boolean expression can be obtained by replacing AND(.) with are OR(+) and vice versa, 1 with 0and vice versa keeping the variables and complements and variables unchanged.
Example; the duality of A.B' + C is A + B'.C
# Law of Boolean Algebra
◼ Identity Laws
➡ A + 0 = A, A.1 = A
◼ Complement Law
➡ A + A' = 1, A.A' = 0
◼ Idempotent Law
➡ A + A = A, A.A = A
◼ Boundedness Law
➡ A + 1 = 1, A.0 = 0
◼Absorption Law
➡ A + (A.B) = A, A.(A + B) = A
◼ Commutative Law
➡ A + B = B + A, A.B = B.A
◼ Associative Law
➡(A + B) + C = A + (B + C), (A.B).C = A.(B.C)
◼ Distributive Law
➡ A.(B + C) = A.B + A.C, A + (B.C) = (A + B) . (A + C)
◼ Involution Law
➡ (A')' = A
◼ De Morgan's Law
➡ i. (A + B)' = A'B' | ii. (A.B)' = A' + B'
● We prove only Identity Law, complement law, commutative law, associative law, distributive law and De Morgan's theorem as per the requirement of curriculum.
