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Let N be the set of natural numbers and a relation R on N be defined by R = {(x, y) ∈ N × N : x3 - 3x2y - xy2 + 3y3 = 0}. Then the relation R is
  • a)
    reflexive and symmetric, but not transitive
  • b)
    reflexive but neither symmetric nor transitive
  • c)
    an equivalence relation
  • d)
    symmetric but neither reflexive nor transitive
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let N be the set of natural numbers and a relation R on N be defined b...
x3 - 3x2y - xy2 + 3y3 = 0
 x(x - y) (x + y) - 3y (x - y) (x + y) = 0
 (x - 3y) (x - y) (x + y) = 0
Now, x = y ∀(x, y) ∈ N × N, hence reflexive
But not symmetric & transitive
(3, 1) satisfies but (1, 3) does not.
Also, (3, 1) and (1, -1) satisfy but (3, -1) does not.
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Most Upvoted Answer
Let N be the set of natural numbers and a relation R on N be defined b...
Sorry, but I can't generate a response based on incomplete information. Can you please provide the complete definition of the relation R?
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Let N be the set of natural numbers and a relation R on N be defined by R = {(x, y)∈N × N : x3- 3x2y - xy2+ 3y3= 0}. Then the relation R isa)reflexive and symmetric, but not transitiveb)reflexive but neither symmetric nor transitivec)an equivalence relationd)symmetric but neither reflexive nor transitiveCorrect answer is option 'B'. Can you explain this answer?
Question Description
Let N be the set of natural numbers and a relation R on N be defined by R = {(x, y)∈N × N : x3- 3x2y - xy2+ 3y3= 0}. Then the relation R isa)reflexive and symmetric, but not transitiveb)reflexive but neither symmetric nor transitivec)an equivalence relationd)symmetric but neither reflexive nor transitiveCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let N be the set of natural numbers and a relation R on N be defined by R = {(x, y)∈N × N : x3- 3x2y - xy2+ 3y3= 0}. Then the relation R isa)reflexive and symmetric, but not transitiveb)reflexive but neither symmetric nor transitivec)an equivalence relationd)symmetric but neither reflexive nor transitiveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let N be the set of natural numbers and a relation R on N be defined by R = {(x, y)∈N × N : x3- 3x2y - xy2+ 3y3= 0}. Then the relation R isa)reflexive and symmetric, but not transitiveb)reflexive but neither symmetric nor transitivec)an equivalence relationd)symmetric but neither reflexive nor transitiveCorrect answer is option 'B'. Can you explain this answer?.
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