Final answer:
A set of temperatures at which water is liquid, under standard atmospheric pressure, is represented by the interval (0°C, 100°C) in interval notation.
Step-by-step explanation:
A set of temperatures at which water is liquid, using interval notation, is (0°C, 100°C). This range is under standard atmospheric conditions where the pressure is about 101.3 kPa. It is in this range that water exists in its liquid phase. This interval doesn't include 0°C and 100°C since at these points water coexists as either solid and liquid or liquid and gas, respectively.
Using the phase diagram of water, we can specifically see that under a pressure of 50 kPa and a temperature of 50 °C, water is in the liquid state. Also, at 25 kPa and 90 kPa with temperatures of 25 °C and 50 °C respectively, water remains as a liquid. These specific conditions fit within the general liquid range of water temperatures.