Important PropertiesThe Engineer
posted on October 23, 2006 |
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:
||Ì belongs to, or is contained in
||E complement of E
||Union and intersection of sets are commutative; that is,
A ? B = B ? A
A B = B A
||Union and intersection of sets are associative; that is,
(A ? B) ? C = A ? (B ? C)
(A B) C = A (B C)
||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.
Copyright © 1975, by John Wiley & Sons, Inc.
This material is used by permission of John Wiley & Sons, Inc.
|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.