JEE Main202430 Jan 2024Evening ShiftMathematicsSets and RelationsActual

The number of symmetric relations defined on the set 1 , 2 , 3 , 4 which are not reflexive is _______.

Correct answer

Step-by-step solution

We know that, Total number of relation both symmetric and reflexive = 2 n 2 - n 2 , where n is number of elements in given set, Also, total number of symmetric relation = 2 n 2 + n 2 Then number of symmetric relation which are not reflexive will be, = 2 n ( n + 1 ) 2 - 2 n ( n - 1 ) 2 = 2 10 - 2 6 = 1024 - 64 = 960

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