# Development of the symbol for the complement of the set B in A

Complement of the set B in A is indicated as A\B (see$_1$). Is there any significance for this slanted version of the symbol? Who first introduced it?

Source: $_1$ Fundamental Concepts of Abstract Algebra by Gertrude Ehrlich.

## 2 Answers

See ISO 31-11 part of international standard ISO 31 (1992) that defines mathematical signs and symbols for use in physical sciences and technology :

$A \setminus B$ : difference between $A$ and $B$; $A$ minus $B$. The set of elements which belong to $A$ but not to $B$.

$A \setminus B = \{ x ∣ x ∈ A ∧ x ∉ B \}$

$A − B$ should not be used.

Originally was $A-B$; from Hausdorff (1927, 1937), Kuratowski (1933) and Bourbaki (1939-1957), to Halmos (1960) and Devlin (1979, 1993).

Originally a set difference was written $A - B$. But of course when $A,B$ are sets of numbers, that may also mean $\{a-b : a \in A , b \in B\}$. So it is confusing. To reduce confusion, one can see $A \sim B$ for this subtraction, or (most common nowadays) $A \setminus B$ as you note.

(I have no information on who first used it.)