Q. 7. Is the power set P(H), which is the set of all subset of H = {1, 2} with the operations of * and *' aBoolean algebra? Justify your answer. Here the operations * and *' on P(H) are defined by:C*D=(CUD)-(CND), and C*' D =(CND), for all C,De P(H).Here U and N represent union and intersection, respectively.Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z.,+6,×6) a field? Justify your answer.Q. 9. List two famous mathematicians and discuss their contributions in mathematics.

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Answered: Q. 8. Show that (Z,,+6,×6) is a…

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Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z,,+6,×6) a field? Justify your answer.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 23E

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Q. 7. Is the power set P(H), which is the set of all subset of H = {1, 2} with the operations of * and *' a
Boolean algebra? Justify your answer. Here the operations * and *' on P(H) are defined by:
C*D=(CUD)-(CND), and C*' D =(CND), for all C,De P(H).
Here U and N represent union and intersection, respectively.
Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z.,+6,×6) a field? Justify your answer.
Q. 9. List two famous mathematicians and discuss their contributions in mathematics.

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