Download PDF by Fazlollah M. Reza: An Introduction to Information Theory

By Fazlollah M. Reza

ISBN-10: 0486682102

ISBN-13: 9780486682105

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E2-3 Verify the relation (A + B)'C = C - C(A + B) Solution. We may wish to verify the validity of this relation by using the Venn diagram of Fig. E2-4. The left side of this equation represents the part of the set C that is not in A or B. The right side represents C - CA - CB, that is, the part of C that is not included either in A or in B. FIG. E2-4 28 DISCRETE SCHEMES WITHOUT MEMORY Example Consider the circuit of Fig. E2-5. :'j which must be activated for or opening the corresponding relay. are normally open relays and A', B', and C' are normally closed relays which are respectively activated by the same controlling source.

C = {6,7,lO} (A + B·C={8,10} 0' = {1,2,3,4,51 B) + 0 = U - {5} 2.. 4. of Sets. We now state certain important properties concerning operations with sets. Let A, B, and C be subsets of a universal set U; then the following laws hold. BASIC CONCEPTS OF DISCRETE PROBABILITY FIG. AB 2-8. Distributive law. A (B + AC. + C) = FIG. 2-9. Distributive law. ---..... /' " A '\. "- 2-10. FIG. --. ,, ~~~ (A /' - ....... / r \ '\. ,A "- "'- + B)' = FIG. A'B'. A' ......... "" B'. A+B=B+A AB = BA Associaiioe Laws: +C = A + + C) (AB)C = A(BC) Distributive Laws: A(B A + + BC + C) = AB AC = (A B)(A C) + + Complementarity: A + A' == U 0 A+U=U AA' = AU = A A +0= A A0 = - 2-11.

The desired set A is See Fig. E2-3. FIG. Example 2-4. E2-3 Verify the relation (A + B)'C = C - C(A + B) Solution. We may wish to verify the validity of this relation by using the Venn diagram of Fig. E2-4. The left side of this equation represents the part of the set C that is not in A or B. The right side represents C - CA - CB, that is, the part of C that is not included either in A or in B. FIG. E2-4 28 DISCRETE SCHEMES WITHOUT MEMORY Example Consider the circuit of Fig. E2-5. :'j which must be activated for or opening the corresponding relay.

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An Introduction to Information Theory by Fazlollah M. Reza


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