Can I deploy an iOS 5.1 SDK app to a device running iOS 6.0 from Xcode?

You can still deploy the older apps but not using Xcode. Instead, you'll need to create an ipa archive and install it either via iTunes, or using a tool such as Testflight or some other over the air (OTA) distribution.

First of all, try to go to Xcode Organizer (small icon in the upper right corner) and see there if you can enable your device for development (click on the device and then its details should appear). There is a chance that this will download all the necessary stuff to allow Xcode to use your newer iOS device (debugging symbols and things like that).

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