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Laws of Boolean Algebra

Law of boolean

# Boolean Postulates
According to Boolean Postulates of Boolean Algebra,

OR lawAND lawNOT law
A + 0 = AA.1 = A0' = 1
A + 1 = 1A.0 = 01' = 0
A + A= AA.A = AA'' = A
A + A' = 1A.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.