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A={1,2,3}

  1. no.of relations possible antisymmetric relations which are not reflexive = …………………..
  2. no.of relations which is antisymmetric but not symmetric=………………………..

No of antisymmetric relation : 2^n * 3^((n^2 – n)/2) ————–(1) no of antisymmetric rel which are reflexive as well is : 3^((n^2 – n)/2) ………(2) To get the answer of 1st question do eq. 1 – eq. 2 where ‘n’ is no of element in the set. no of antisymmetric rel which are symmetric as well is : 2^n ……………..(3) To get the answer of 2nd question do eq. 1 – eq. 3 where ‘n’ is no of element in the set.

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