Question

Let $S$ be the set of all points in a plane and $R$ be a relation in $S$ defined as $R=\left\{\right(a,b):$ distance between points $a$ and $b$ is less than $2$ units $\}$

The relation $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. equivalence

Answer 1

Answer: (A), (B)

The correct options are
A symmetric
B reflexive

Distance between $a$ and $a$ is $0,$ which is less than $2$ units.
$R$ is reflexive.
If $(a,b)\in R$, then distance between $a$ and $b$ is less than $2$ units
$\Rightarrow$ Distance between $b$ and $a$ is less than $2$ units

$(b,a)\in R$

$\therefore R$ is symmetric