By Fazlollah M. Reza

ISBN-10: 0486682102

ISBN-13: 9780486682105

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When a finite number or a countably infinite number of events A 2, • • • , An are mutually independent, * we have (2-86) * The events AI, A 2, • • • ,An are said to be statistically independent of each other when the probability of any of these events and the probability associated with the intersection of any number of these events do not depend on any other event except those occurring in the intersection. That is, P{AiA j} = P{Ai}P{A j} P{AiAjAkl = P{A,;}P{AilP{Akl for all combinations of i, i, and k satisfying 1-5:i

14) (2-15) 24 DISCRETE SCIIEMES WITHOUT MEMORY For the convenience of the we shall to latter notations. 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.

Solution. 6 The set that corresponds to the operation of the circuit in Fig. 6b is (A + B)(A' + B') Direct multiplication gives AA' + AB' + BA' + BB' == AB' + A'B The latter set can be immediately identified with the circuit of Fig. 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.

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