Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Mcq Single Correct #39
For real numbers \(x,y\), write \(xRy\iff x-y+\sqrt{2}\) is irrational. The relation \(R\) is
✅ Step-by-Step Solution
Final Answer: Option (A): Reflexive
- \(x-x+\sqrt2\) is irrational, so reflexivity holds. Symmetry fails for \(x=\sqrt2,y=0\). Transitivity fails for \(x=0,y=\sqrt2/2,z=\sqrt2\): the first two differences plus \(\sqrt2\) are irrational, but the third is 0.
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