On the lee side of the mountain, is the relative humidity of the
parcel increasing or decreasing as it descends fro 6000 feet to sea
level?

True

Explanation:

As the windward side of the mountain gets lots of rainstorms and coming winds thus this side remains windy and rainy, as compared to the leeward side the mountain barrier acts as a system that obstructs and stops the flow of winds and thus keeping this area high and dry. Due to the moisture-laden winds fall on the west side of the mountains and so unable to get carried away from their source towards the other eastern end. The leeward side remains warm and relative more humid. Thus, for this reason, this area is called the rain shadow region.