set difference (original) (raw)

Definition

Let A and B be sets. The set difference (or simply difference) between A and B (in that order) is the set of all elements of A that are not in B. This set is denoted by A∖B or A-B(or occasionally A∼B). So we have

Properties

2. 1. If A and B are sets, then
3. 1. If A and B are subsets of a set X, then
      and
      where ∁ denotes complement in X.
4. 1. If A, B, C and D are sets, then

Remark

As noted above, the set difference is sometimes written as A-B. However, if A and B are sets in a vector space(or, more generally, a module (http://planetmath.org/Module)), then A-B is commonly used to denote the set

rather than the set difference.