Problem 2 Let R be a relation on a set A Prove or disprove I

Problem 2 Let R be a relation on a set A. Prove or disprove: If R is antisymmetric, then R is irreflexive.

Solution

we can disprove thiswith help of counter example

let\'s suppose we have a set R with elements { (3,3), (4,4) }

now we know that R is anti symmetric if xRy and yRx and x =y , which clearly is the case , so it is antisymmetric,

what we see here that the elements are reflexive i.e xRx here so we have clearly got an counter example , where the set is antisymmetric and reflexive.