UIL Official List of Boolean Algebra Identities (Laws)
1 A A  A
2 A* A  A
3 A B  B  A
4 A* B  B * A
5 A  ( B  C )  ( A  B)  C
6 A * ( B * C )  ( A * B) * C
7 A * ( B  C)  A * B  A * C
8 A  B * C  ( A  B) * ( A  C )
9 A 1  1
10 A * 0  0
11 A * ( A  B)  A
12 A  A * B  A
13 A * 1  A
14 A  0  A
Indempotent Law for OR
Indempotent Law for AND
Commutative Law for OR
Commutative Law for AND
Associative Law for OR
Associative Law for AND
Distributive Law for AND over OR
Distributive Law for OR over AND
Law of Union
Law of Intersection
Law of Absorption
Law of Absorption
Identity Law for AND
Identity Law for OR
15
A A
Double Negative Law
16
A A 1
Law of Complement for OR
17
A* A  0
Law of Complement for AND
18
A  B  A* B
DeMorgan's Law
19
A* B  A  B
DeMorgan's Law
20
A  B  A* B  A* B  A* B  A* B
Exclusive OR (XOR)
21
A  B  A* B  A* B
Exclusive NOR (XNOR)
A  A* B  A  B
23 ( A  B) * ( A  C )  A  B * C
22
24
( A  B) * (C  D)  A * C  A * D  B * C  B * D
Law of the "disappearing opposite"
Reverse of Law #8
FOIL (First,Outer,Inner,Last) Distribution
Note: AND will always be expressed explicitly with the * operator
st) Distribution