Why does the cold front turn sunny and the warm wind turn rainy?

According to the physical properties of water, the higher the temperature, the higher the saturated vapor pressure of water and the higher the content of water vapor in the air. The lower the temperature, the lower the saturated vapor pressure of water and the lower the content of water vapor in the air.

When the cold front crosses the border, it brings cold air from the north, with low temperature and little water vapor. Cumulonimbus clouds can't form in the atmosphere, and the weather turns fine.

After the warm wind, it brings warm air in the south, with high temperature and much water vapor, which can form cumulonimbus clouds in the atmosphere and turn to rain.