1.II.5B
(a) Find a subset of the Euclidean plane that is not fixed by any isometry (rigid motion) except the identity.
Let be a subgroup of the group of isometries of a subset of not fixed by any isometry except the identity, and let denote the union . Does the group of isometries of contain ? Justify your answer.
(b) Find an example of such a and with .
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