Set difference

Definition · applies to sets · also called $A \setminus B$, relative complement

High school

Consider1 two sets $A$ and $B$. The set difference $A \setminus B$ is the set of elements of $A$ that are not in $B$.

Examples

Worked examples

• $A = \setdef{1, 2}$ and $B = \setdef{3, 4}$ : $A \setminus B = \setdef{1, 2}$ Elementary

Examples

• $\setdef{1, 2, 3} \setminus \setdef{2} = \setdef{1, 3}$ Elementary
  $\setdef{1, 2, 3} \setminus \setdef{2}$ is a set difference because it removes the elements of $\setdef{2}$ from $\setdef{1, 2, 3}$.

Distinctions involving this term

• Types of difference: Many quantities compare two things by “how far apart” they are. A difference is the result of subtraction and can be negative. No distance is negative. An error compares an approximation with the truth, a change compares the end with the start, and a set difference removes elements.

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