7. Let H = {1, 5} and two operations * and *' on H defined as follow:151511111155Is (H, *. *') a Boolean algebra? Justify your answer8. Show that (Z,,×s) is a monoid. Is (Z,,×6) an abelian group? Justify your aI

Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Let H = {1,5} and two operations * and on H defined as follow: %3D 15 15 1 11 1 15 5 15 5 5 Is (H, *. *) a Boolean algebra? Justify your answer Show that (Z,,x6) is a monoid. Is (Z,,x6) an abelian group? Justify your a

Let H = {1,5} and two operations * and on H defined as follow: %3D 15 15 1 11 1 15 5 15 5 5 Is (H, . ) a Boolean algebra? Justify your answer Show that (Z,,x6) is a monoid. Is (Z,,x6) an abelian group? Justify your a

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 6E

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7. Let H = {1, 5} and two operations * and *' on H defined as follow:
15
15
1
1
1
1
1
1
5
5
Is (H, *. *') a Boolean algebra? Justify your answer
8. Show that (Z,,×s) is a monoid. Is (Z,,×6) an abelian group? Justify your aI

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