Boolean Theorems/Laws (A1.2 Data representation and computer logic)

Commutative law

Operations are the same so the order can be changed

A.B = B.A

A+B = B+A

Idempotent law

Variable combined with itself is itself

B.B = B

B+B = B

Involution law

Negation of negation results in just the original variable

(A')' = A

Associative law

Operations done to a group are the same means that order can change

A.(B.C) = (A.B).C

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

Absorption law

A.(A+B) = A

A+(A.B) = A

A'+AB = A'+B

Distributive law

Variable can be distributed among a group

A.(B+C) = (A.B)+(A.C)

A+(B.C) = (A+B).(A+C)

Complement law

A.A' = 0