Xcode 5 is behaving just fine, and I\'m able to build and run apps on my iOS 7 device and in the iOS 7 simulator.
However, I do want to support iOS 6.1, but I don\'t
All you have to do is go to Xcode -> Preferences -> Choose the "Downloads" tab and install the iOS 6.0 Simulator.
Once you're done downloading it, it should show up as an option in your schemes.
What I did to get mine working was click on the scheme to the left of where the Simulators usually appear in the dropdown, then choose edit scheme.
A new window will display, make sure that Run is highlighted on the left and then click on the Info tab. Choose the .app file for Executable.
Click to target or project > Build Settings > Achitecture > Supported Plateforms : change to iOS
Solved restoring an older version of the xcodeproj file.
Please check whether your "Deployment Target" is higher than the ones available on your simulators.