JEE Exam  >  JEE Questions  >  Let R be the relation defined in the set A = ... Start Learning for Free
Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R is
    • a)
      an equivalence relation
    • b)
      non commutative relation
    • c)
      a universal relation
    • d)
      an empty relation
    Correct answer is option 'A'. Can you explain this answer?
    Verified Answer
    Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by ...
    Consider any a ,b , c ∈A .
    1. Since both a and a must be either even or odd, so (a , a) ∈R ⇒ R is reflexive.
    2. Let (a ,b) ∈R ⇒ both a and b must be either even or odd, ⇒ both b and a must be either even or odd, ⇒ (b ,a) ∈R .Thus , (a ,b) ∈R ⇒ (b ,a) ∈R ⇒ R is symmetric.
    3. Let (a ,b) ∈R and (b ,c) ∈R ⇒ both a and b must be either even or odd, also ,both b and c must be either even or odd, ⇒ all elements a, b and c must be either even or odd, ⇒ (a ,c) ∈R . Thus, (a ,b) ∈R ⇒ (b,c) ∈R ⇒ (a ,c) ∈R ⇒ R is transitive.
    View all questions of this test
    Explore Courses for JEE exam
    Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer?
    Question Description
    Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. 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 R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. 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 R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer?.
    Solutions for Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. 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 R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R isa)an equivalence relationb)non commutative relationc)a universal relationd)an empty relationCorrect answer is option 'A'. 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