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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

  1. R is symmetric, transitive but not reflexive    
  2. R is only transitive    
  3. R is symmetric, reflexive but not transitive    
  4. R is neither reflexive nor transitive but is symmetric.    

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

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