Exact results are found using the 'replica' method, for the zero-temperature phase diagram of a random Ising system with the nearest-neighbour exchange coupling having probabilities p, q and r of being positive, negative or zero. The system exhibits paramagnetic (PM), ferromagnetic (FM), antiferromagnetic (AFM) and spin-glass (SG) phases. The concentrations for which the transitions FM to SG and AFM to SG (at r=0) and PM to SG (p=q) occur are exactly calculated for various lattices in two and three dimensions. The former has Ising model exponents, and the latter has exponents of the s-state Potts model with s to 1/2. Crossover effects to finite temperatures are discussed. The results in the ordered phases are shown to be problematic, since they do not allow frustrated bonds. This casts light on the limitations of the 'replica' method.