Refer to figure.
STEAMING FOG (ARCTIC SMOKE). occurs over sea, mainly in polar regions.

• It is caused when cold air from a land mass moves over a (comparatively) warmer sea (water surface) = advection of VERY cold air over a warm sea. The small amount of evaporation from the sea is enough to cause saturation and condensation, before the water has warmed up the lower level of air. The difference in temperature between air and water has to be more than 10°C.
• Steam fog is typically up to 500 feet thick and may drift inland.
• Forms in conditions of no wind or very light winds. Will be dispersed by an increase in wind speed or change of direction.

As for this question, then, we are looking for a large temperature difference between the water and the air over water. As we do not know the water temperature in most of these examples, we can instead estimate it based on the effect that the water has had on the air over land (AOL) temperature. If the temperature of the air over water (AOW) is higher than air over land (AOL), then the water has warmed the air up, and is therefore warmer than the land.

Also, we know the minimum temperature of water is 0°C, as otherwise it would be ice.

• “Air over water: 5°C, air at 2 000 ft: -5°C, land temp: 5°C.”
  • INCORRECT → No change between AOW and AOL.
• “Air over water: -5°C, air at 2 000 ft: 0°C, land temp: 10°C.”
  • INCORRECT → AOW is colder than AOL here, which is not right.
• “Air over water: 0°C, air at 2 000 ft: -5°C, land temp: -10°C.”
  • POSSIBILITY 1 → The AOW is warmer than AOL, by 10 degrees.
• “Air over water: -15°C, air at 2 000 ft: -20°C, land temp: -18°C.”
  • POSSIBILITY 2 → The AOW is slightly warmer than AOL, indicating slow warming by the water. Also, given the extremely low AOW temperature, we know that the minimum temperature difference between water and AOW is 15°C.

Possibility 2 gives the best conditions for steam fog (Arctic sea smoke) as it is very cold, and the water is slowly warming the air above it, but will be inputting more moisture into the incredibly cold air faster than it can warm it up, saturating it quickly, which is a key requirement for steam fog.

As for the requirement for an inversion, it is almost impossible to tell if an inversion is present here, as it usually arises between the ground and approximately 500 ft, so the 2000 ft temperature is not much of a sign. Also, the only case of inversion here has a seemingly much colder AOW than AOL, which doesn't work.