Theorems of Boolean Algebra:
Identity:
A + 0 = A
A. 1 = A
Complement:
\(A+\overline{A}=1\)
\(A.\overline{A}=0\)
Commutative:
A + B = B + A
A. B = B .A
Associative:
A + (B + C) = (A + B) + C
A. (B . C) = (A. B). C
Distributive
A. (B + C) = A B + A. C
A + (B . C) = (A + B). (A + C)
Null Element:
A + 1 = 1
A. 0 = 0
Involution
Indempotence:
A + A = A
A.A = A
Absorption:
A + (A . B) = A
A . (A + B) = A
3rd Distributive:
\(A + \overline{A}. B = A + B\)
De Morgan’s:
\(\overline{A+B}=\overline{A.B}\)
\(\overline{A.B}=\overline{A}+\overline{B}\)
