# Proofs in Group Theory : Cayley Table, Subsets and Cosets - Five Problems

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Five Problems:

Let G=[FORMULA1], with operation given by multiplication modulo 14.

1) by computing the Cayley table of G, or otherwise, show the G is a group. You may assume that without proof multiplication modulo 14 is associative.

2) Prove that the subset H={1,9,11} is a subgroup of G

3) Compute the left cosets of G and H ...

(Please see attachment for proper citation of formulas and for problems 4 and 5).

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#### Solution Summary

Cayley Table, subsets and cosets are investigated. The solution is well presented.

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