An Introduction to Information Theory by Fazlollah M. Reza

By Fazlollah M. Reza

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We assume that the measure associated with an event, in the case of the repeated experiment, is proportional to the number of the outcomes in the event under consideration. In essence, this assumption makes the frequency definition somewhat too restrictive. 2-9. Theorem of Addition. It seems appropriate now to continue with BASIC CONCEPTS OF DISCRETE PROBABILITY our formalism without restriction to an immediately but slow procedure. For two events A and B of the sample space one has A V (B - AB) = A V B The additive property of the probability measure in Sec.

E2-6b. Sheffer-stroke Operation. Examples 2-5 and 2-6 have illustrated some use of Boolean algebra in relay circuits. As another example of the use of BASIC CONCEPTS OF DISCRETE PROBABILITY 0+-=--FIG. (XI Y) 2-12. Sheffer stroke. Boolean algebra in problems, we discuss what is referred to as the Sheffer-stroke operation. This operation for two sets X Y is denoted by (XI Y) and is defined by the equation (XI Y) = X' U Y' not X, or not Y, or not X and Y The Sheffer stroke commonly illustrated by the three-port diagram of Fig.

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.

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