Determine which of the following define equivalence relations in R2. For those that do, give a geometrical interpretation of the quotient set.
(a) (a, b) ~ (c, d) if and only if a + 2b = c + 2d.
(b) (a. b) ~ (c. d) if and only if al? = cd.
(c) (a, b) ~ (c, d) if and only if a2 + b = c -f d2.
(d) (a, b) ~ (c, d) if and only if a = c.
(e) (a, b) ~ (c, d) if and only if cib - c2.
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