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For each of the following relations on the set of all real numbers, decide whether or not the relation is reflexive, symmetric, antisymmetric, and/or transitive. Give a brief explanation of why the given relation either has or does not have each of the properties. (x, y) E R if and only if: (1) x + y = 0
(2) x – y is a rational number (a rational number is a number that can be expressed in the form a/b where a and b are integers)
(3) x = 2y
(4) xy >= 0

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