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JEE Main20231 Feb 2023Morning ShiftMathematicsSets and RelationsActual

Let R be a relation on ℝ , given by R = a , b : 3 a - 3 b + 7 is an irrational number . Then R is

Options

  1. AReflexive but neither symmetric nor transitive
  2. BReflexive and transitive but not symmetric
  3. CReflexive and symmetric but not transitive
  4. DAn equivalence relation

Correct answer

A. Reflexive but neither symmetric nor transitive

Step-by-step solution

Given: R = a , b : 3 a - 3 b + 7   is   irrational Reflexive: 3 a - 3 a + 7 = 7 is irrational. So, a , a ∈ R , hence R is reflexive. Given: R = a , b : 3 a - 3 b + 7   is   irrational Symmetric: Let a , b ∈ R , then 3 a - 3 b + 7 is irrational. So, 3 b - 3 a + 7 is not necessarily irrational, since if 3 a = 7 and 3 b ∈ Z , then 3 a - 3 b + 7 is irrational., but 3 b - 3 a + 7 is not irrational. So, a , b ∈ R ⇒ b , a ∈ R , hence R is not symmetric Transitive: Ta

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