Given that,
it is ir-reflexive ===> (x,x) not allowed.
it is symmetric and transitive ===> if (x,y) is in R, then (y,x) must be present in R.
But note that as per transitive if (x,y) and (y,x) is present in R, then (x,x) must be in R, but we can't have such pairs due to ir-reflexive.
∴ R can be only EMPTY SET ===> |R| = 0