The correct explanation for why valley air moves up surrounding mountains during the day is:
The Sun warms the air in the valley more than it does the mountains.
During the day, the sunlight heats the ground, and as the valley air becomes warmer, it becomes less dense and rises. This process creates a convection current that allows the warmer valley air to ascend the slopes of the surrounding mountains. The air over the mountains may not warm as significantly because they often have a higher altitude and can have more shade from surrounding features, leading to the observed upward movement of the warmer valley air.