Important Properties
Staff posted on October 23, 2006 |
Important Properties

Sets and the relationship among sets are governed by certain operational rules. In this connection, we adopt the following symbols to designate sets or their associated operations:

 È union n intersection Ì belongs to, or is contained in É contains E complement of E

 Commutative rule. Union and intersection of sets are commutative; that is, A ? B = B ? A A B = B A Associative rule. Union and intersection of sets are associative; that is, (A ? B) ? C = A ? (B ? C) (A B) C = A (B C) Distributive rule. Union and intersection of sets are distributive; that is, (A ? B) C = A C ? B C (A B) ? C = (A ? C) (B ? C) de Morgan's rule. Excerpt from: Ang, Alfredo H-S. and Tang, Wilson H. Probability Concepts in Engineering Planning and Design. New York: John Wiley & Sons, Inc., 1975.

 Venn Diagram Venn Diagrams can be used to illustrate the differences between unions, intersections, and complements. The union of A and B consists of all element belonging to either A or B, denoted by A ? B. The D represents a domain and U is a universal set of D. The intersection of A and B consists of elements that belong to both A and B, denoted by A n B. The Complement of A consist of elements belong to A, denoted by À. 