Sets, Relations and Function: Which of the following is not correct for relation R on the set of… | JEE Main 2021

JEE Main 2021 (Online) 31st August Morning ShiftQuestion 1

Which of the following is not correct for relation $R$ on the set of real numbers ?

Sets, Relations and Function

$(x,y)\in R\Leftrightarrow|x-y|\le1$ is reflexive and symmetric.$(x,y)\in R\Leftrightarrow|x|-|y|\le1$ is reflexive but not symmetric.$(x,y)\in R\Leftrightarrow0<|x|-|y|\le1$ is neither transitive nor symmetric.$(x,y)\in R\Leftrightarrow0<|x-y|\le1$ is symmetric and transitive.✓ Correct answer

Solution

(D): $0<|x-y|\le1$ is symmetric but not transitive: $(0,0.8),(0.8,1.6)\in R$ but $(0,1.6)\notin R$. So (D) is incorrect; (A),(B),(C) are correct. Option (D).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2021 (Online) 31st August Morning Shift)

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