Laws of Boolean Algebra

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Boolean algebra consists of two binary operations + and., unary operation, two distinct element 0 and 1, and variables that holds 0 and 1. Following are different laws of Boolean algebra.

Lets a,b,c be Boolean variables then

1. Identity Laws 

a) a + 0 = a                                b) a.1 = a

2. Complement Laws

a) a + a' = 1                                b) a.a' = 0

3. Idempotent Laws

a) a + a = a                                b) a.a = a

4. Boundedness Laws 

a) a + 1 = 1                                b) a.0 = 0

5. Absorption Laws 

a) a + (a.b) = a                            b) a.(a + b) = a

6. Commutative Laws 

a) a + b = b + a                            b) a.b = b.a

7. Associative Laws 

a) (a + b) + c = a + (b + c)            b) (a.b).c    = a.(b.c)

8. Distributive Laws

a) a + (b.c) = (a + b). (a + c)         b) a.(b + c) = (a.b) + (a.c)

9. Involution Law

    (a')' = a

10. De-Morgan's Laws

a) (a + b)' = a'.b'                            b) (a.b)' = a' + b'

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