Final answer:
A negative dS implies a decrease in system entropy, but during reversible processes, such a decrease is countered by a greater increase in the surroundings' entropy, leading to a net increase in the universe's entropy.
Step-by-step explanation:
If dS is negative, it indicates a decrease in entropy of a system. However, in thermodynamics, when a system undergoes a reversible process and loses heat (-drev) to the surroundings, the magnitudes of the heat lost by the system and the heat gained by the surroundings are equal, but they have opposite signs. This heat transfer happens at different temperatures, where the system has a higher temperature (Tsys) than the surroundings (Tsurr). In such cases, even though the entropy of the system decreased, the increase in entropy of the surroundings will be greater because entropy is inversely related to temperature. Therefore, after considering both the system and surroundings, the total entropy of the universe increases.