Let N be the set of natural numbers and a relation R on N be defined by R= (x, y) N N: x^…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
Let N be the set of natural numbers and a relation R on N be defined by
\(R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .\)
Then the relation R is:
\(R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .\)
Then the relation R is:
- reflexive and symmetric, but not transitive
- reflexive but neither symmetric nor transitive
- an equivalence relation
- symmetric but neither reflexive nor transitive
Answer
(B) reflexive but neither symmetric nor transitive
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