Complement

The Complement at U+2201 denotes the mathematical complement of a set, relation, or logical condition. It sits in the Mathematical Operators block and is used as an operator meaning “everything in the relevant universe except this.” Its most common role is in set theory and discrete mathematics, where ∁A means the complement of set A relative to an understood universal set. For example, if U is all integers and A is the even integers, ∁A is the odd integers; many textbooks also write this as A′, Aᶜ, or U \ A. The symbol also appears in logic, probability, and computer science when an event, predicate, or language is negated by taking what is outside it. In probability, ∁E can mean “not E,” so P(∁E) = 1 − P(E); in automata theory, the complement of a language contains exactly the strings over the alphabet that the original language does not contain. Because several complement notations are more common than this standalone operator, ∁ is often seen in formal reference material, theorem statements, and symbolic math systems rather than in everyday classroom handwriting. It can be mistaken for a stylized C, but its meaning depends on a surrounding universe or domain being clear.