Reciprocal Dunford--Pettis sets and V^*-sets in Banach lattices

In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V^*-sets in a Banach lattice. That is, for a bounded subset K of a Banach lattice E, K is a V^*-set if and only if K is a reciprocal Dunford--Pettis set, or equivalently, if and only if every disjoint sequence in the solid hull of K is weakly null (i.e. K is disjointly weakly compact).