JEE Exam  >  JEE Questions  >  Let N be the set of natural numbers and a rel... Start Learning for Free
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?
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?
Free Test
Community 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.
Explore Courses for JEE exam
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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev