Question No. 1: Let R be the relation on the real numbers given by xRy iff |x-y|≤2. Prove that this relation is Reflexive, Symmetric but not transitive.
Question No. 2: Define a relation ~ on R by, x~y if x-y is rational. Prove that ~ is an equivalence relation.
Question No. 3: Define a relation P that is reflexive but not symmetric and not transitive
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