R is a relation on R defined by xRy if x-Y+√2 is an irrational number.
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No ; not at all . Because xRy iff (x+y)/xy or 1/x + 1/y >/= 0 for x, y belonging to Q, is not even defined when either x = 0 or y = 0 . Thus R is not even a relation, so no question arise of being any thing else like equivalence relation etc.
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