definitely the less than relation won't be reflexive bcz a<a is always false for every a belongs to real number.
now for antisymmetric (a<b & b<a) implies a=b , as we know if a<b then b<a can never be true at once therefore (a<b & b<a) results false. but false can implies anything therefore it is antisymmetric.
for a relation to be POSET: it must be reflexive, antisymmetric and transitive
here it is not reflexive but antisymmetric in nature therefore only E option is correct.