In recent years, research has moved from traditional query processing (e.g., Selection, Nearest Neighbor (NN), Top-k, Skyline), to reverse query processing (e.g., Reverse NN, Reverse Top-k, Reverse Skyline), to maximal reverse query processing (e.g., find spatial points that maximize the number of Reverse NNs), and so on. This paper considers the Smallest Set Reverse Selection Queries Problem also known as the Multiple Tuple Design Problem: Given a set of selection queries with conjunctive conditions, where the task is to create the smallest set of tuples such that each query returns at least one of these tuples. The problem is an interesting variant of the Maximal Reverse Selection Queries Problem (also referred to as the Tuple Design Problem) introduced by Miah et al. (2016). The paper shows that the problem is NP-Complete and develops approximation algorithms with provable approximation guarantees, as well as carefully designed heuristics that work well in practice. The paper also designs efficient exact algorithm that are feasible for moderate instances. It provides extensive experiments that demonstrate the effectiveness of the proposed algorithms.