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JEE Main202312 Apr 2023Morning ShiftMathematicsSets and RelationsActual

The number of relations, on the set 1 , 2 , 3 containing 1 , 2 and 2 , 3 which are reflexive and transitive but not symmetric, is _________.

Correct answer

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Step-by-step solution

Given, Set A = 1 , 2 , 3 Now Cartesian product A × A = 1 , 1 , 2 , 1 , 1 , 2 , . . . . . . . . , 3 , 3 Now, given the relation is reflexive, So, 1 ,   1 ,   2 ,   2 ,   3 ,   3   ∈   R Also given 1 ,   2 ,   2 ,   3 ∈   R ,   1 ,   3 must ∈   R Now finding, Possible cases : Case-1 : All of 2 ,   1 ,   3 ,   2 ,   3 ,   1   ∉ R → 1 relation. Case-2: Only one of 2 ,   1 ,  

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