In the paper we investigate whether the function-independent test set for detecting single stuck-at faults in networks realising Reed-Muller canonic (RMC) expansions of switching functions is sufficient to detect all bridging faults in such networks. The investigation, however, reveals its insufficiency, and to circumvent this we propose a technique of augmenting the network with some additional observation points, so that a universal test set can be designed for detecting bridging faults as well.