Definition: Set Intersection
Let $A$ and $B$ be sets. Based on the conjunction operation "\(\wedge\)", the set intersection of \(A\) and \(B\) is defined as \[A\cap B:=\{x  x\in A\wedge x\in B\}.\]
The intersection contains all elements \(x\), which are contained in both, \(A\) and \(B\). It can be visualized by a Venn diagram like this:
Examples
 Let $A=\{1,2,3,4\}$ and let $B=\{3,4,5,6\}.$ Then the intersection set is $A\cap B=\{3,4\}$. Please note that we do not have to list the repeating elements twice in the intersection set.
 The intersection of the set of countries of Europe and the set of the countries of Asia is the set of all countries belonging to both, Asia and Europe, i.e. the set $\{\text{Azerbaijan}, \text{Georgia}, \text{Kazakhstan}, \text{Russia},\text{Turkey}\}$^{1}.
Table of Contents
 Definition: Disjoint Sets
 Proposition: Intersection of a Set With Another Set is Subset of This Set
 Proposition: Set Intersection is Commutative
 Proposition: Set Intersection is Associative
Mentioned in:
Axioms: 1
Corollaries: 2
Definitions: 3 4 5 6 7
Explanations: 8
Lemmas: 9
Parts: 10
Proofs: 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Propositions: 30 31 32 33 34 35 36 37 38 39
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References
Bibliography
 Reinhardt F., Soeder H.: "dtvAtlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
 Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016
Footnotes