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    Equation

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    6. Let (G, *) be a group. Show that each equation of either the form ax = b or the form xa = b has a unique solution in G.

    7. Show that (R - {1}, *), where a * b = a + b + ab is a group

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    https://brainmass.com/math/discrete-math/equation-functions-groups-60254

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    6. Let (G, *) be a group. Show that each equation of either the form ax = b or the form xa = b has a unique solution in G.

    7. Show that (R - {1}, *), where a * b = a + b + ab is a group

    [Recall:

    Let G is a non-empty set, A binary operation * together with G defined as (G,*) is called a "Group" if the following properties hold in G:

    G1: Closure property:

    a * b  G for each a  G and b G

    G2: Associative property:

    a*(b*c) = (a*b)*c for each a G, b G and c G

    G3: Existence of identity element:

    a*e = e *a = a , e is the identity element in G.

    G4: Existence of inverse element:

    For each a G, there exists an ...

    Solution Summary

    This solution is comprised of a detailed explanation to show that each equation of either the form ax = b or the form xa = b has a unique solution in G.

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