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.

Copyright © 1975, by John Wiley & Sons, Inc.

This material is used by permission of John Wiley & Sons, Inc.

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.

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