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Maths-

General

Easy

Question

Let $A equals left curly bracket A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma A subscript 4 end subscript comma A subscript 5 end subscript comma A subscript 6 end subscript right curly bracket$ be the set of six unit circles with centres $C subscript 1 end subscript comma C subscript 2 end subscript comma C subscript 3 end subscript horizontal ellipsis C subscript 6 end subscript$ arranged as shown in the diagram. The relation $R$ on A is defined by $left parenthesis A subscript i end subscript comma A subscript j end subscript right parenthesis element of R less than rightwards double arrow C subscript i end subscript C subscript j end subscript less or equal than 2 square root of 2$ then

$R$ is symmetric, transitive but not reflexive
$R$ is only transitive
$R$ is symmetric, reflexive but not transitive
$R$ is neither reflexive nor transitive but is symmetric.

The correct answer is: $R$ is symmetric, reflexive but not transitive

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