Explain why the following binary relations on S = {1, 2, 3} is not an equivalence relation on S.

R = {(1, 1), (2,2), (3, 3), (2, 1),(1, 2), (2, 3) , (3, 1), (1, 3)}

Determine, with reasons, whether or not each of the following defines an equivalence relation on the set A.

a) A is the set of all circles in the plane: a ~ b if and only if a and b have the same center.

b) A is the set of all straight lines in the plane: a ~ b if and only if a is parallel to b.

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