The complementary law describes the AND and OR operations of a variable with the corresponding inverted variable.

The **complementary law** of an **AND** operation reads...

$$A \wedge \neg A = 0$$

The **complementary law** of an **OR** operation reads...

$$A \vee \neg A = 1$$

Comparison Arithmetic - Boolean Algebra
The complementary law applies to the $$x + (-x) = 0 $$
The complementary law |