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JEE Main20238 Apr 2023Evening ShiftMathematicsSets and RelationsActual

Let A = 1 , 2 , 3 , 4 , 5 , 6 , 7 . Then the relation R = ( x , y ) ∈ A × A : x + y = 7 is

Options

  1. Aan equivalence relation
  2. Bsymmetric but neither reflexive nor transitive
  3. Ctransitive but neither symmetric nor reflexive
  4. Dreflexive but neither symmetric nor transitive

Correct answer

B. symmetric but neither reflexive nor transitive

Step-by-step solution

We have, A = 1 , 2 , 3 , 4 , 5 , 6 , 7 Reflexive : A relation R on a set A is said to be reflexive if every element of A is related to itself. Thus, R   is   reflexive ⇔ ( a , a ) ∈ R   for   all   a ∈ A ∵ ( 1 , 1 ) , 2 , 2 , ( 3 , 3 ) , . . . . . . ( 7 , 7 ) does not satisfy x + y = 7 Hence R is not reflexive. Symmetric : A relation R is symmetric on a set A iff ( a , b ) ∈ R ⇒ ( b , a ) ∈ R   for   all   a , b ∈ A ⇒ x +

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