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JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R\,= \{(x,y) : x,y \in N\, and\, x^2 -4xy +3y^2\, =0\}\), where \(N\) is the set of all natural numbers. Then the relation \(R\) is
- A reflexive but neither symmetric nor transitive
- B symmetric and transitive
- C reflexive and symmetric,
- D reflexive and transitive
Answer & Solution
Correct Answer
(D) reflexive and transitive
Step-by-step Solution
Detailed explanation
\(R = \left\{ {\left( {x,y} \right):x,y \in N\,\,and\,\,{x^2} - 4xy + 3{y^2} = 0} \right\}\) Now, \({{x^2} - 4xy + 3{y^2} = 0}\) \( \Rightarrow \left( {x - y} \right)\left( {x - 3y} \right) = 0\) \(\therefore x = y\) or \(x = 3y\)…
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