Definition: Set Difference
Let $A$ and $B$ be sets. The set difference of the sets \(A\) and \(B\) is defined using the conjunction operation "\(\wedge\)",
\[A\setminus B :=\{x \mid x\in A \wedge x\notin B\}.\]
It is the set of all elements contained in \(A\) and not contained in \(B\). The following Venn diagram shows a set difference:
Examples:
- The set difference $A\setminus B$ of the set $A=\{2,3,4,7,8,9\}$ and $B=\{1,2,3\}$ equals $\{4,5,6,9\}.$
- The set difference $A\setminus B$ of the set $A=\{2,3,4,7,8,9\}$ and $B=\{1,2,3\}$ equals $\{4,5,6,9\}.$
Mentioned in:
Corollaries: 1 2
Definitions: 3
Explanations: 4
Lemmas: 5
Parts: 6
Proofs: 7 8 9 10 11 12
Propositions: 13
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References
Bibliography
- Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
- Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016
