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Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_relations

Class 12 Maths · Relations And Functions · Mcq Single Correct #119

For real numbers \(x,y\), define \(xRy\) if and only if \(x-y+\sqrt2\) is irrational. Then \(R\) is

✅ Step-by-Step Solution

Final Answer: Option (A): Reflexive
  1. Every \(xRx\) holds because \(\sqrt2\) is irrational. Symmetry fails for \(x=\sqrt2,y=0\). Transitivity fails for \(0,\sqrt2/2,\sqrt2\): the first two related pairs hold, but the final expression is 0.

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