Boolean Logic Cheat Sheet

English Math and EE Formal Circuit

And (Conjunction) A ·B A ∧B

Or (Disjunction) A+B A ∨B

Not (Negation) !A, A ¬A, ∼ A

Table 1: Operations and Notations

A B A ·B A+B A

0 0 0 01

0 1 0 11 0 0 1

01 1 1 1

Table 2: Truth Tables

1

Associativity

A+ (B + C) ⇐⇒ (A+B) + C

A · (B · C) ⇐⇒ (A ·B) · C

Distributivity

A · (B + C) ⇐⇒ (A ·B) + (A · C)

A+ (B · C) ⇐⇒ (A+B) · (A+ C)

Commutativity

A ·B ⇐⇒ B ·A

A+B ⇐⇒ B +A

De Morgan’s Law

A ·B ⇐⇒ A+B

A+B ⇐⇒ P ·Q

Table 3: Laws of Boolean Algebra

Name Rule

1aIdempotency

A ·A = A

1b A+A = A

2aIdentity

A+ 0 = A

2b A · 1 = A

3aBoundedness

A+ 1 = 1

3b A · 0 = 0

4aComplement Laws

A+A = 1

4b A ·A = 0

5aAbsorption

A+A ·B = A

5b A ·A+B = A

6 Involution A = A

7aConsensus Theorem

A ·B +A · C +B · C = A ·B +A · C

7b (A+B) · (A+ C) · (B + C) = (A+B) · (A+ C)

Table 4: Derived Rules

2