I should use region monitoring in my iOs app for 6 and 7 version. And if my app was closed then system should open it. It works in iOS 6, but not works in iOS 7. I mean, Sys
This is now the expected behaviour starting with iOS7. In iOS6 and earlier, even if you manually killed the app from the app-switcher, you would still get a notification when the user entered/exited a region. This behaviour has changed with iOS7. If the user has killed the app from the app-switcher, i.e. by swiping up on your app, then they will no longer receive any location-based notifications, including region monitoring notifications. This was confirmed by an Apple Employee in the official Apple developer forums - link here.
The only solution provided by Apple Dev was "Please file bug reports if this change is problematic for you or you would like to see something different."
I personally think this was a terrible decision, as it defeats the purpose of background notifications. You will have to advise your users upgrading from iOS6, as they will continue to expect similar functionality and this change has not been documented anywhere.
EDIT: As @herz below has pointed out, starting in iOS 7.1, the background monitoring functionality has reverted to how it was in iOS 6. Regions will be monitored and your app will receive notifications even when it is killed from the app switcher.