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Does it make sense to run a dehumidifier in the basement when you have air conditioner running through a couple vents at the same time. It seems like you are defeating the purpose and adding to your electric bill for no reason.
What's the humidity level in the basement? Regardless of whether or not the AC is running, there is no reason to run the dehumidifier if the humidity is at a reasonable level. Yes, the AC should reduce the humidity in the basement (based upon the vents in the basement), but if it isn't lowering the humidity enough, then the dehumidifier may be needed.
Most good dehumidifiers will turn on and off depending on the humidity setting. An air conditioner will remove some moisture but is not designed as a dehumidifier.