The air conditioner is used to dessicate (dry) the air so that the air itself will hold more moisture when it passes over the foggy windshield because damp air will not dry wet stuff as quickly.
The air conditioner condenses the moisture out of the air much like how a iced drink gets wet on the outside from moisture in the air condensing on the cold surface of the glass. this is why there is water dripping underneath the car when the a/c is running.
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