**Laws of Boolean Algebra**

According to the laws of Boolean Algebra, we use some variables, i.e. (A, B, C, X, Y, Z), and Apply NOT, AND, OR operations on these variables.

**Types of Laws in Boolean Algebra **

There are several laws of Boolean algebra, which are given below; let’s explain all equations of these laws with proof through the Truth Table.

**1. Commutative Law**

According to commutative law

- Any order in which two variables are AND’ed makes a similar result always (i.e., A . B = B . A )
- Any order in which two variables are OR’ed makes a similar result always (i.e., A + B = B + A)

**2. Associative Law**

- A.(B.C) = (A.B).C = A . B . C (AND Associate Law)
- A + (B + C) = (A + B) + C = A + B + C (OR Associate Law)

**3. Distributive Law**

- A.(B + C) = (A.B) + (A.C) (OR Distributive Law)
- A + (B.C) = (A + B) . (A + C) (AND Distributive Law)

**4. Annulment law**

According to Annulment Law

- A variable AND’ed with 0 will always be equal to 0 (i.e., A . 0 = 0)
- A variable OR’ed with 1 will always be equal to 1 (i.e. A + 1 = 1)

**5. Identity law**

According to Identity Law

- A variable OR’ed with 0 will always be equal to that variable (i.e., A + 0 = A)
- A variable AND’ed with 1 will always be equal to that variable (i.e., A . 1 = A)

**6. Idempotent law**

According to idempotent law

- A variable OR’ed with itself will always be equal to that variable (i.e., A + A = A)
- A variable AND’ed with itself will always be equal to that variable (i.e., A . A = A )

**7. Complement law**

According to complement law

- A variable AND’ed with its complement will always equal to 0. (i.e., A . A’ = 0)
- A variable OR’ed with its complement will always equal to 1. (i.e. A + A’ = 1)

**8. Double Negation law**

According to the double negation law

- The double complement of a variable will always equal that variable. (i.e. (A’)’ =A)

**9. Absorption law**

- A + (A.B) = A (OR Absorption Law)
- A . (A+B) = A (AND Absorption Law)

**10. De Morgan’s Law**

According to De Morgan’s law

- (A.B)’ = A’ + B’
- (A+B)’ = A’
**.**B’