Problem 3. (5 x 4 points) For the following problems, prove or disprove that R is an equivalence relation. Remember, an equivalence relation is reflexive, symmetric, and transitive. To show that a relation is not an equivalence relation, show that one of these properties does not hold via a counterexample. (a) R = {(a, b) c R x R|a= ]] (b) R = {(a, b) | Purdue student a is taking a same class as Purdue student b) (c) R = [(a, b) CR2 x R' | a = (a1, a2), b= (b1,by), an = bi], where R' = RX R = = = (#1, $2) |21, 12 ( R). Note that this is simply a projection of a vector c ( R- onto the I. axis. (d) R - {(a, b) CRt x Rt [ a' + 4a + 5,a > b' + 46 + 5vb)