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By Fazlollah M. Reza

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HH) , (HT), (TH), (TT) where H denotes head and T denotes tail. A may assume that his chances of winning the game are %, since a head occurs in three out of four cases (to his advantage). On the other hand, the following reasoning may also seem logical. If the outcome of the first throw is H, A wins; there is no need to continue the game. Accordingly, only three possibilities need be considered, namely: (H), (TH), and (TT) where the first two cases are favorable to A and the last one to B. other words, the probability that A wins is really % instead of %.

Difference A-B. The complement or negation of any set A is the set A I containing all elements of the universe that are not elements of A. In the mathematical literature the following notations are commonly used in conjunction with the above definitions. A V B A (\ B A - B B A A I'J A union B, or A cup B A intersection B, or A cap B relative complement of B in A B is contained in A complement of A In the engineering literature the notations given below are . . used. 14) (2-15) 24 DISCRETE SCIIEMES WITHOUT MEMORY For the convenience of the we shall to latter notations.

E2-5 A way of simplifying the above expression is the following: F = C(AB + AB' + A'B') F = C[A(B + B') + A'B'] F = C(AU + A'B') F = C(A + A'B') F = C(A + B') A circuit presentation of this example is illustrated in Fig. 5b. Example 2-6. Verify the equivalence of the two relay circuits of Fig. E2-6. A B' B (a) (b) FIG. 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.

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