Duality in logical algebra: If all "+","+","0" and "1" in logical function expression F are changed to "+"and "1" are changed to "0", while the operation order in the original function remains unchanged, the new logical expression obtained is called duality of function F, for example, f = ab. It can be seen from the example that if the dual form of F is f', then the dual form of f' is F, that is, F and f' are dual to each other.

If the dual form of a logical function expression is the original function expression itself, that is, f'= f, then the function f is called a self-dual function. For example, a function is a self-dual function. Because: f' = (A C+B) (A C) = (A B) (C B) (A B) (A C) = A (B C) (A C)+B (B C) (A C).

If two logical function expressions f and g are equal, then their dual expressions f' and g' are also equal. This rule is called the double rule. According to the law of duality, when two logical expressions are proved to be equal, we can know that their dual expressions are also equal. For example, AB+AC+BC=AB+AC is known.

According to the law of duality, we know that the dual expressions at both ends of the equation are also equal, that is, (a+b) (a+c) (b+c) = (a+b) (a+c).