Question: Let R be the relation on Z+ defined by: for all x, y Z+, x R y if and only if gcd(x, y) = 1.

Let R be the relation on Z+ defined by: for all x, y Z+, x R y if and only if gcd(x, y) = 1. (a) Is R reflexive? Is R symmetric? Is R transitive? Explain. (b) Prove or disprove: for all x, y Z+ if x R y, then (x + 2y) R (2x + 3y). (c) Prove or disprove: for all x, y Z+ if x R y, then (x + y) R (2x + 4y).

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