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If we define a relation R on the set N×N as (a,b) R (c,d)⇔a+d=b+ c for all (a,b),(c,d)‎∈‎N×N, then the relation is
  • a)
    Symmetric only
  • b)
    Symmetric and transitive only
  • c)
    Equivalence relation
  • d)
    Reflexive only
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If we define a relation R on the set N×N as (a,b) R (c,d)⇔a...
(a,b) R (c,d)⇔a+d=b+c
⇒(a,a) R (a,a)⇒R is reflexive
∵ a+a=a+a
Next, Let (a,b) R (c,d)⇒a+d=b+c
⇒c+b=d+a⇒(c,d) R (a,b)
⇒ R is symmetric.
Next, Let (a,b) R (c,d) and  (c,d) R (e,f)
⇒ a+d=b+c and c+f=d+e
⇒ a+d+c+f=b+c+d+e
⇒ a+f=b+e⇒(a,b) R (e,f)
⇒ R is transitive ⇒ R is an equivalence relation.
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If we define a relation R on the set N×N as (a,b) R (c,d)⇔a+d=b+ c for all (a,b),(c,d)‎∈‎N×N, then the relation isa)Symmetric onlyb)Symmetric and transitive onlyc)Equivalence relationd)Reflexive onlyCorrect answer is option 'C'. Can you explain this answer?
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If we define a relation R on the set N×N as (a,b) R (c,d)⇔a+d=b+ c for all (a,b),(c,d)‎∈‎N×N, then the relation isa)Symmetric onlyb)Symmetric and transitive onlyc)Equivalence relationd)Reflexive onlyCorrect answer is option 'C'. 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 If we define a relation R on the set N×N as (a,b) R (c,d)⇔a+d=b+ c for all (a,b),(c,d)‎∈‎N×N, then the relation isa)Symmetric onlyb)Symmetric and transitive onlyc)Equivalence relationd)Reflexive onlyCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If we define a relation R on the set N×N as (a,b) R (c,d)⇔a+d=b+ c for all (a,b),(c,d)‎∈‎N×N, then the relation isa)Symmetric onlyb)Symmetric and transitive onlyc)Equivalence relationd)Reflexive onlyCorrect answer is option 'C'. Can you explain this answer?.
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