Boolean Algebra

Propositional logic is the basis of Boolean algebra.
The values are true and false, and logical operators are used.

Let T = true and F = false.
The dot operator is conjunction, the AND (dot is often left off);
plus operator is disjunction, the OR.

Basic operations

If p != F then p = T 
If p != T then p = F 
T · T = T 
T + T = T 
F · F = F 
F + F = F 
F · T = T · F = F 
F + T = T + F = T 
!T = F,  !F = T 

Boolean algebra theorems

Let T = true and F = false.

Commutative law:  p · q = q · p,   p + q = q + p
Associative law:  (p · q) · r = p · (q · r),    (p + q ) + r = p + (q + r)
Distributive law: (p + q) · (p + r) = p + (q · r),  p · q + p · r = p · (q + r)
Annulment law:    P · F = F,   p + T = T
Identity law:     p · T = p,   p + F = p
Complement law:   p · !p = F,   p + !p = T
Square law:       p · p = p,   p + p = p
Absorption law:   p · (p + q) = p,   p + p · q = p
Double negative:  !(!p) = p
DeMorgan's law:   !(p · q) = !p + !p,   !(p + q) = !p · !q