Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Mcq Single Correct #42
On \(\mathbb{R}\), define \(xRy\iff x^2=xy\). Which statement is correct?
✅ Step-by-Step Solution
Final Answer: Option (B): Reflexive and transitive but not symmetric
- Every real \(x\) satisfies \(x^2=x\cdot x\), so the relation is reflexive. If \(xRy\) and \(yRz\), either \(x=0\), which implies \(xRz\), or \(x\ne0\), in which case \(y=x\ne0\) and then \(z=y=x\). Thus it is transitive. It is not symmetric: \(0R1\), but not \(1R0\). The repaired option b is the unique correct classification.
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