Editing Set (mathematics) (section)

===Set difference===
[[File:Venn0100.svg|thumb|<div class="center">The ''set difference'' {{math|''A'' \ ''B''}}</div>]]
The ''set difference'' of two sets {{tmath|A}} and {{tmath|B}}, is a set, denoted {{tmath|A \setminus B}} or {{tmath|A - B}}, whose elements are those elements that belong to {{tmath|A}}, but not to {{tmath|B}}. That is,
<math display=block>A \setminus B=\{x\mid x\in A \land x\not\in B\},</math>
where {{tmath|\land}} denotes the [[logical and]]. 

[[File:Venn1010.svg|thumb|<div class="center">The ''complement'' of ''A'' in ''U''</div>]]
When {{tmath|B\subseteq A}} the difference {{tmath|A \setminus B}} is also called the ''[[set complement|complement]]'' of {{tmath|B}} in {{tmath|A}}. When all sets that are considered are subsets of a fixed ''universal set'' {{tmath|U}}, the complement {{tmath|U \setminus A}} is often called the ''absolute complement'' of {{tmath|A}}.

[[File:Venn0110.svg|thumb|<div class="center">The ''symmetric difference'' of ''A'' and ''B''</div>]]
The ''[[symmetric difference]]'' of two sets {{tmath|A}} and {{tmath|B}}, denoted {{tmath|A\,\Delta\,B}}, is the set of those elements that belong to {{mvar|A}} or {{mvar|B}} but not to both:
<math display =block>A\,\Delta\,B = (A \setminus B) \cup (B \setminus A).</math>