Q63 / 125 · BITSAT 2013 · Mathematics

Let $R$ be the relation on the set $R$ of all real numbers, defined by $a R b$ If $|a-b| \leq 1$. Then, $R$ is

  • Correct answer
    A
    reflexive and symmetric only
  • B
    reflexive and transitive only
  • C
    equivalence
  • D
    None of the above

Solution

Since, $|a-a|=0 \leq 1,$ so $a R a, \forall a \in R$ $\therefore R$ is reflexive. Now, $a R b \Rightarrow|a-b| \leq 1 \Rightarrow|b-a| \leq 1 \Rightarrow b R a$ $\therefore R$ is symmetric. But $R$ is not transitive as $1 R 2,2 R 3$ but $1 \not R^{\prime} 3$ $$ [\because|1-3|=2>1] $$

Hence, the correct answer is option: 'A'.

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