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Maths-

General

Easy

Question

Let $blank A equals open curly brackets A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma A subscript 4 end subscript comma A subscript 5 end subscript comma A subscript 6 end subscript close curly brackets$ 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 $open parentheses A subscript i end subscript comma A subscript j end subscript close parentheses element of R left right double arrow C subscript i end subscript C subscript j end subscript less or equal than 2 square root of 2 text end text$ then
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/839751/1/1167938/Picture1.png" alt="" width="98" height="79"

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

$open parentheses C subscript i end subscript comma C subscript i end subscript close parentheses equals 0 less or equal than 2 square root of 2 R text is reflexive end text$
$open parentheses A subscript i end subscript comma A subscript j end subscript close parentheses element of R rightwards double arrow C subscript i end subscript C subscript j end subscript less or equal than 2 square root of 2 rightwards double arrow C subscript j end subscript C subscript i end subscript less or equal than 2 square root of 2$
$therefore open parentheses A subscript j end subscript comma A subscript i end subscript close parentheses element of R$
R is symmetric
$text if end text open parentheses A subscript 1 end subscript comma A subscript 2 end subscript close parentheses element of R comma open parentheses A subscript 2 end subscript comma A subscript 3 end subscript close parentheses element of R rightwards double arrow open parentheses A subscript 1 end subscript comma A subscript 3 end subscript close parentheses not an element of R$

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