MATH 271 Final: MATH 271 Amherst S16m271Final

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1. (3 points each) answer the following questions by giving careful de nitions. De ne: f is a partition of a: (7 points each) write the following statements using logical symbols. Susan rice was wrong about benghazi only if the state department politicized the talking points. A necessary condition for hillary clinton to be the next president is that the state department did not politicize the talking points. Brie y explain the error: (9 points) prove that for all n 1, n. 1: (9 points) suppose that r and s are equivalence relations on a set a and r s. Prove that for all x a/r there is some y a/s such that x y : recall that z+ = the set of all positive integers = {1, 2, 3, . R = {(x, y) z+ z+ | j z+(x j = y and j is odd)}.