Set difference (A ∖ B)
A ∖ B, read “A minus B”, is the set difference: the elements of A that are not in B. It is also written A − B.
Easily confused with
How to read it
Oscar Levin’s Discrete Mathematics defines A ∖ B as the set of all elements of A which are not elements of B: start with A and remove everything that is also in B. It is the same as A ∩ B̄, the part of A outside B. The order matters. OpenStax’s Contemporary Mathematics, using the minus-sign form, works an example: with A = {a, b, c, d} and B = {b, d, f, h}, A − B = {a, c} but B − A = {f, h}. NIST’s Digital Library of Mathematical Functions calls ∖ “set subtraction”, and Unicode names it SET MINUS (U+2216).
Also searched as: A ∖ B, A - B sets, A minus B, backslash in sets, relative complement, set minus.
∖ or −
Both are in use. Levin and NIST write the slanted ∖; the Sets Challenge app that OpenStax mentions uses the minus sign. Taken from the universal set, U ∖ A is the Complement of a set (A′) A′.
Look-alikes
The set minus leans the same way as the keyboard backslash \, and Unicode cross-refers the two, but they are separate characters; Unicode also lists the reverse solidus operator ⧵ (U+29F5) and the mathematical falling diagonal ⟍ (U+27CD) as look-alikes.
Read next
- Next in Set theory symbolsEmpty set symbol (∅)∅ is the empty set, also called the null set: the set with no elements. It can also be written as a pair of empty braces, { }.
- The same shape in Barcodes and QR codesCode 128 and GS1-128Code 128 is a barcode that can hold any letter, digit or keyboard symbol, so it turns up on shipping and warehouse labels. GS1-128 is the GS1 version, where each piece of data starts with an Application Identifier printed in brackets.
More set theory symbols
The same shape elsewhere
Browse symbols drawn with letters and numbers or lines.
Sources
- Discrete Mathematics, 0.3 Sets, Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd edition, Oscar Levin, University of Northern Colorado (Open Math Books), Set theory notation; set difference
- Contemporary Mathematics, 1.4 Set Operations with Two Sets, OpenStax (Rice University), Sets Challenge notation
- NIST Digital Library of Mathematical Functions: Introduction (Common Notations and Definitions), U.S. National Institute of Standards and Technology, Common Notations and Definitions
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Miscellaneous mathematical symbols, 2216
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
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