Question

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

• A. Reflexive and Symmetric
• B. Symmetric only
• C. Transitive only
• D. Anti-symmetric only

Answer 1

The correct option is A Reflexive and Symmetric

$|a-a|=0<1\therefore aRa\forall aϵR$
$\therefore$ R is reflexive.
Again $aRb\Rightarrow |a-b|\le 1\Rightarrow |b-a|\le 1\Rightarrow bRa$
$\therefore R$ is symmetric.
Further, 1 R 2 and 2 R 3 but $1\text{/}R3,[\because |1-3|=2>1]$
$\therefore R$ is not transitive.