A low pressure system will also have a high humidity due to the formation of water vapour being easier in a lower atmospheric pressure even at the lower temperatures which accompany them.
This type of system will generally bring high winds and precipitation.
High pressure systems are generally much drier and calmer with less to no cloud formations and brighter skies.
There is not a question being asked here. If you are asking for confirmation, then you have explained the situation quite nicely. I am glad that you included the word "generally" in your descriptions, because it is possible to have a high pressure system with high humidity. More or less the entire state of Florida would be a good example of this. It's location is closer to the equator than any other state in the continental United States, so that makes temperatures there quite warm. Additionally, Florida is surrounded by ocean on three sides. This makes the air mass that typically forms over Florida a warm and wet air mass. Meteorologists would call it maritime tropical.
Conversely it is possible to have a cold, low pressure air mass that is low in humidity. A lot of Canada has this because it is tundra. The air mass over this region is typically dry because it is over a continent and cold because it is so far north. The technical jargon describing that air mass would be continental polar.
The other part of your statement that I want to clarify is that low pressure systems tend to have higher relative humidity. As air temperature falls, the air gets denser and denser; therefore, there is less space available for holding water. If no moisture leaves the air, and the air isn't able to hold as much water vapor, the percentage of relative humidity goes up. Think about it this way. If I only put 1 quart of water in a 1 gallon jug, the jug is 25% full. But if I put that same quart of water in a half gallon jug, the jug is 50% full. Air is the same way. X amount of water vapor might be 20%, 50%, or 90% humidity depending on how warm the air is and how much water the air is capable of holding at that temperature. Low pressure, cold air systems may have a higher relative humidity, but that doesn't mean the air is actually holding more moisture.