Let R be a relation from ℝ (set$$ of real $$numbers) to ℝ defined by $$R={(a$$,$$b)$$∣a,b∈ℝ and a−$$b+3$$ is an irrational number $$}$$ . The relation R is

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Let R be a relation from ℝ (set$$ of real $$numbers) to   ℝ defined by   $$R={(a$$,$$b)$$∣a,b∈ℝ and a−$$b+3$$ is an irrational number $$}$$ .  The relation R  is

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$$R={(a$$,$$b)$$∣a,b∈R and a−$$b+3$$ is an irrational number $$}$$, then R is reflexive since $$aRa=a$$−$$a+3=3$$ which is an irrational number  $$3R$$ $$1=3$$−$$1+3=23$$−$$1$$ which  is an irrational number but    $$1$$ $$R3$$  $$=1$$−$$3+3=1$$ which is not irrational number  ∴R is not symmetric  AlsoR is not transitive            $$($$  ∵$$3R1$$     and    $$1R23$$    but     $$3R23$$                                                           ⇒$$3$$−$$23+3=0$$  $$)$$ Hence, R is not an equivalence relation

$Let R be a relation from ℝ (set of real numbers) to ℝ defined by R = {(a, b) ∣ a, b \in ℝ and$ $a - b + \sqrt{3} is an irrational number} . The relation R is$

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Let R be a relation from ℝ (set of real numbers) to ℝ defined by R={(a,b)∣a,b∈ℝ and a−b+3 is an irrational number } . The relation R is

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$Let R be a relation from ℝ (set of real numbers) to ℝ defined by R = {(a, b) ∣ a, b \in ℝ and$ $a - b + \sqrt{3} is an irrational number} . The relation R is$