What is the difference between dual and complement?

Dual and complement are concepts used in different contexts within mathematics and computer science. The dual of a mathematical expression or structure typically refers to a corresponding structure that reflects its properties in a different way, often through a transformation that interchanges certain elements, such as in linear programming or lattice theory. In contrast, the complement refers to the counterpart of a set or logical statement, representing elements not included in the original set or the negation of a logical proposition. Essentially, duality involves a structural relationship, while complementation involves opposition or exclusion.