# Boolean Algebra Laws

The **boolean postulates** that we are going to learn in this chapter serves as the basic axioms of the algebraic structure.

The postulates don't need any proof and are used to prove the theorems of boolean algebra.

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These postulates are also referred to as** laws of boolean **algebra.

### Postulate 1

- X = 0, if and only if, X is not equal to 1
- X = 1, if and only if, X is not equal to 0

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**Postulate 2**

- a + 0 = a
- a.1 = a

The above postulate is referred as identity law of boolean algebra.

**Postulate 3**

- a + b = b + a
- a.b = b.a

The above postulate is referred as **commutative law** of boolean algebra.

**Postulate 4**

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

The above postulate is referred as **associative law** of boolean algebra.

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**Postulate 5**

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

The above postulate is referred as **distributive**** **law of boolean algebra.

**Postulate 6**

- a + a' = 1
- a . a' = 0

The above postulate is referred as complement law of boolean algebra.

These postulates are the core of the boolean algebra.

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