In set theory, the complement of a set A, often denoted by $${\displaystyle A^{c}}$$ (or A′), is the set of elements not in A. When all elements in the universe, i.e. all elements under consideration, are considered to be members of a given set U, the absolute complement of A is the set of elements in U that are not in A. The relative complement of A with respect to a set B, also termed the set difference of B and A, written $${\displaystyle B\setminus A,}$$ is the set of elements …

DefinitionIf A and B are sets, then the relative complement of A in B, also termed the set difference of B and A, is the set of elements in B but not in A. The relative complement of A in B is denoted $${\displaystyle B\setminus A}$$ according to the ISO 31-11 standard. It is sometimes written $${\displaystyle B-A,}$$ but this notation is ambiguous, as in some contexts (for example, Minkowski set operations in functional analysis) it can …