Let Tors be the category whose objects are torsion abelian groups; if and are torsion abelian groups, we define to be the set of all (group) homomorphisms . Prove that direct products exist in Tors; that is, show that given any indexed family where is a torsion abelian group, there exists a torsion abelian group which serves as a direct product for this family in Tors.