Boolean Dual

The dual of a Boolean or of a Boolean expression is obtained by applying 2 operations: replacing/interchanging the logical ORs by logical ANDs and vice versa and replacing/interchanging the logical 0s by logical 1s and vice versa.

Example: The dual of a+b is a.b and conversely the dual of a.b is a+b (duality principle)

It is possible that the value $ a $ itself has a dual, some note this dual $ a' $ (be careful not to confuse this notation with the boolean NOT unary operator)

The dual of a boolean function $ F $ is sometimes denoted by $ Fˊ $ (not to be confused with the complement or NOT function) or $ F ^ d $.

Likewise 0 and 1 are dual, true and false are duals, ∧ and ∨ are dual.

Every Boolean expression has a dual, the Boolean Duality principle means that every theorem or any computation has a dual equivalent.

By proving something in Boolean algebra, its dual is also proved.

Example: x+1=1 has for dual x.0=0