The Nature of Mathematics, 12th Edition
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Section 2.2: Operations with Sets

2.2 Outline

A.  Fundamental operations
      1. intersection; "and"
      2. union; "or"
B. Cardinality of intersections and union
      1. Venn diagram for union
      2. Formula 

2.2 Essential Ideas 

Operations with Sets

Remember the basic operations:

Complement

The complement of a set S is consists of everything that is not in S.

Union

The union of two sets is everything that is in either set; that is, anything colored (blue, yellow, or green).

Intersection

The intersection of two sets is everything that is in both sets; that is, anything colored both blue and yellow, namely green.

Cardinality of Intersections and Unions
The cardinality of an intersection is the number of elements in the intersection.
The cardinality of a union is the sum of the cardinalities of the given sets less the number of elements in the intersection.

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