Unions (∪) and Intersections (∩)

Lets start exploring the various relationships between sets. Lets look at the first two type: the union and intersection of two sets. The union of two sets A and B is the collection of elements which are in A or in B or in both A and B (1). The symbol ∪ (2) is used to represent this concept in mathematical statements.  Such a relationship can also be expressed using a Venn diagram (3).   The orange areas represent the union of both sets. Given two sets, there is sometimes the need to know what elements the sets have in common. The intersection of two sets A and B is s a math term used to describe the collection of elements which are in A and B (1).  In mathematical statements, the symbol ∩ (2) is used to represent this concept. This concept of intersection can also be expressed in a Venn Diagram (3).  The orange area represents the intersection of Set A and B.

Lets visually consider two random lines, A and B, that are not parallel to each other. Set A is the collection of all points that make up line A. Set B is the collection of all points that make up line B. In Euclidian geometry, two line that are not parallel will always intersect each other. In this case, the intersection of Sets A and B consists of one point and only one point. Such visual representation of intersections  are found on all street maps. If you are out and about, you will notice that the intersection of any two streets represents the section of road that both streets have in common.

Most of the basic symbols of logic and set theory in use today were introduced between 1880 and 1920. The symbols ∩ and ∪ were introduced by Giuseppe Peano (1858-1932), an Italian mathematician, for intersection and union in Calcolo geometrico (“Geometrical Calculus”) secondo l’Ausdehnungslehre di H. Grassmann (1888).

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