Clear explanation of the Boolean laws with simple examples

⚡ Boolean Laws – Simple Explanation ⚡

🔹 1. Commutative Law

Definition: The order of variables does not affect the result.

A + B = B + A
A · B = B · A

1 + 0 = 0 + 1 = 1
1 · 0 = 0 · 1 = 0

🔹 2. Associative Law

Definition: The grouping of variables does not affect the result.

(A + B) + C = A + (B + C)
(A · B) · C = A · (B · C)

(1 + 0) + 1 = 1 + (0 + 1) = 1
(1 · 0) · 1 = 1 · (0 · 1) = 0

🔹 3. Distributive Law

Definition: Multiplication distributes over addition and vice versa.

A · (B + C) = (A · B) + (A · C)
A + (B · C) = (A + B) · (A + C)

1 · (0 + 1) = (1·0) + (1·1) = 1
1 + (0·1) = (1+0)(1+1) = 1

🔹 4. Redundancy Law (Absorption)

Definition: Extra terms can be removed without changing the result.

A + (A · B) = A
A · (A + B) = A

1 + (1·0) = 1
1 · (1 + 0) = 1

🔹 5. De Morgan’s Theorem

Definition: Used to simplify expressions with NOT operation.

(A · B)’ = A’ + B’
(A + B)’ = A’ · B’

(A · B)’ = (1·0)’ = 1
A’ + B’ = 0 + 1 = 1 ✅

(A + B)’ = (1+0)’ = 0
A’ · B’ = 0 · 1 = 0 ✅