Complement (set theory)

A circle filled with red inside a square. The area outside the circle is unfilled. The borders of both the circle and the square are black.
If A is the area colored red in this image…
An unfilled circle inside a square. The area inside the square not covered by the circle is filled with red. The borders of both the circle and the square are black.
… then the complement of A is everything else.

In set theory, the complement of a set A, often denoted by (or A),[1] is the set of elements not in A.[2]

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 is the set of elements in B that are not in A.

  1. ^ "Complement and Set Difference". web.mnstate.edu. Retrieved 2020-09-04.
  2. ^ "Complement (set) Definition (Illustrated Mathematics Dictionary)". www.mathsisfun.com. Retrieved 2020-09-04.