Intersection of Sets
A "and" B

As union, intersection is the another basic operation in algebra of sets. The main difference of this operation with the previous one is the particle "and". It means that in order to form this new set, the elements of the intersection have to belong to both sets (A and B) at the same time. In other words, elements have to coincide in both or more sets.

Obviously, this definition could be difficult to understand without an example.

Let consider an example:

Given that A is the set of prime number smaller than 10 and B is the set of odd numbers smaller than 10. Mathematically, we can express these sets in the following way:

A = {3, 5, 7}

B = {1, 3, 5, 7, 9}

Therefore, the intersection of the sets A and B is given by the following statement:

A "and" B = {3, 5, 7}

Please, note that the elements 3, 5, and 7 are belonging, at the same time, to both sets (A and B).
Again, maps could help us in understand the concept of intersection.

Let consider a map from the University of Illinois at Urbana-Champaign, Quad:

UIUC Quad
Note that it is common talk about intersections among streets when we are observing a map.

In this campus map, Wright Street is perpendicular with Green, John, and Daniel Streets. Commonly, when we are reading a map, we denote the corner of two streets as an intersection of them. Now, take few minutes to locate the Wright Street. At the corner of Wright and Daniel Streets, there is theIllini Union Bookstore (See the arrow on the map). It means that the bookstore is the intersection of these two streets.

Could you mention another intersection in this campus map?

Do you have some another examples in order to illustrate this relationship between sets? If so, could you share them with us?

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