- Edited
Thank you @rogerch! I might be off on this point, and different ACs may work in different ways. I think ShiroKuro explained it well--*although an AC, or air conditioner (yes, I'm thinking of the ones that cool down your house) cools down the air, meaning it can now hold less water and raising the RH, (this causes the RH to rise given the same amount of moisture in the room), it must furst it pass air over a cold coil, which causes condensation out of the air onto the coil (thus reducing the moisture in the air). So it could net out differently depending on efficiency, how long the AC runs, etc.
But if you have an AC that draws in outside air, or one that is oversized and cools down the room very quickly, you could end up in a situation where higher RH air ends up replacing the warm air in your house. I'm sure a number of other things are possible too, depending on the variety of AC/heat pump setups that exist.
In my house, whenever the AC is on, the RH drops precipitously, and my dehumidifer never turns on.
*edited to correct vapor capacity