Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Complement (set theory)
open-in-new
<p>In <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, the complement of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> A, often denoted by A c {\displaystyle A^{c}} (or <i>A</i>′), is the set of <a href="/facts/Element_(mathematics)/Q2mx1vHL">elements</a> not in A. </p><p>When all elements in the <a href="/facts/Universe_(set_theory)/v2oJnu4e">universe</a>, i.e. all elements under consideration, are considered to be <a href="/facts/Element_(mathematics)/Q2mx1vHL">members</a> of a given set U, the absolute complement of A is the set of elements in U that are not in A. </p><p>The relative complement of A with respect to a set B, also termed the set difference of B and A, written B ∖ A , {\displaystyle B\setminus A,} is the set of elements in B that are not in A. </p>