Read e-book online An Introduction to Information Theory PDF

By Fazlollah M. Reza

ISBN-10: 0486682102

ISBN-13: 9780486682105

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For example, let X be the set of all persons living in the state of California on January 1, 1959, and let the function be defined as follows: anyone who is the father of a person described by X and is in the state of Colorado on January 1, 1959. Assuming that all the words appearing in the rule, such as father, California, Colorado, are well-defined words, this may be considered as a well-defined function. To each member of X there corresponds an object in the set Y. In this example, element zero in Y corresponds to some of the elements of X, and several members of X might have a unique correspondent in Y.

RCA implies Af'\B=B (2-17) The sum, the product, and the difference of two sets and the complement of any set A are illustrated in the shaded areas of the Venn diagrams o 2-6. AB == O. FIG. Mutually exclusive sets. FIG. 2-7. Subset B C A. 2-2 to 2-5. Figures 2-6 and 2-7 illustrate the sets and (2-17). Example 2-1. 01"1""I"O' to Let the universe consist of the set of all positive integers, and let A = {1,2,3,6,7,lO} B = {3,4,8,lOI 0= [z ] where x is any positive integer larger than 5. Find A + B, A .

However, where any confusion in notation may occur we resort to mathematical notation. The universe and the empty set will be denoted U and 0,.. ,VV ...... the two sets are said to be mutually exclusive. When the product of the two sets A and B is equal to B, then B is a subset of A. RCA implies Af'\B=B (2-17) The sum, the product, and the difference of two sets and the complement of any set A are illustrated in the shaded areas of the Venn diagrams o 2-6. AB == O. FIG. Mutually exclusive sets.

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An Introduction to Information Theory by Fazlollah M. Reza


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