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  3. consider g = (z12, +). let h = {0, 3, 6, 9}. a. sh

Consider G = (Z12, +). Let H = {0, 3, 6, 9}. a. Show that H...

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Advance Math

Consider G = (Z12, +). Let H = {0, 3, 6, 9}.

a. Show that H is a subgroup of G.

b. Find all the cosets of H in G and denote this set by G/H.[Note: If x ? G then H +12 [x]12 = {[h +x]12?? | [h]12 ? H} is the coset generated byx.]

c. For H +12 [x]12, H +12[y]12 ? G/H define(H+12[x]12)?(H+12[y]12)by(H+12 [x]12)?(H+12[y]12)=H+12 [x+y]12.

d. Show that ? is well defined and construct the addition tablefor G/H with the operation ?.

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