Definition:Relative Complement

Let $$S$$ be a set, and let $$T$$ be a subset of $$S$$.

Then the set difference $$S - T$$ can be written $$\mathcal{C}_S \left({T}\right)$$, and is called the relative complement of $$T$$ in $$S$$, or the complement of $$T$$ relative to $$S$$.

An alternative notation for $$\mathcal{C}_S \left({T}\right)$$ is $$\complement_S \left({T}\right)$$. Some authors use merely $$C T$$ for the relative complement of $$T$$, it being implicit in their notation what the superset of $$T$$ is at the point where this notation is used.

Some authors call this the complement and use relative complement for the set difference $$S - T$$ when the stipulation $$T \subseteq S$$ is not required.