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    Isomorphic proofs

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    1.) G_1 is isomorphic to G_2 and H_1 is isomorphic to H_2 implies G_1/H_1 is isomorphic to G_2/H_2

    2.) G_1 is isomorphic to G_2 and G_1/H_1 is isomorphic to G_2/H_2 implies H_1 is isomorphic to H_2

    3.) H_1 is isomorphic to H_2 and G_1/H_1 is isomorphic to G_2/H_2 implies G_1 is isomorphic to G_2

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    https://brainmass.com/math/discrete-math/isomorphic-proofs-230516

    Solution Preview

    1. Answer : False
    Counter Example: Let , , , then . But we note , . Therefore, is not isomorphic to .
    2. Answer: True
    Proof:
    We ...

    Solution Summary

    This provides examples of completing proofs regarding isomorphisms.

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