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Let R be the relation on the set of all colorings of the 2 × 2 checkerboard where each of the four squares is colored either red or blue

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Let R be the relation on the set of all colorings of the 2 × 2 checkerboard where each of the four squares is colored either red or blue so that (C 1 , C 2 ), where C 1 and C 2 are 2 × 2 checkerboards with each of their four squares colored blue or red, belongs to R if and only if C 2 can be obtained from C 1 either by rotating the checkerboard or by rotating it and then reflecting it.

Solve the following:
a) Show that R is an equivalence relation.
b) What are the equivalence classes of R?
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