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DVI-I:

DVI-I contains both the digital and analog connections, (DVI-D + DVI-A) , it's essentially a combination of DVI-D and DVI-A cables within one cable.
DVI-D:

DVI-D (like DFP or P&D-D (EVC)) is a digital only connection. If both devices being connected support a Digital DVI connection (DVI-I or DVI-D compatible) and are compatible in resolutions, refresh rates and sync, using a DVI-D cable will ensure that you are using a digital connection rather than an analog connection, without playing around with settings to assure this.
DVI-A:

DVI-A is really rare. Why use a DVI connector when you can use a cheaper VGA connector? see DVI-I P&D-A (EVC) is more common with projectors, and you should go to your projector manufacturer for recommendations.
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