Mac won't boot; get the Apple logo then it becomes a prohibitory symbol I start up my early 2011 MacBook Pro, and it gives me the login screen, I enter my password, and then booting starts as normal, but about halfway through the progress bar, it stops booting entirely and comes up with this symbol.



I'm really not sure what to do. In recovery mode I'm unable to access the partition that holds the Mac OS (it's grayed out) and when I try to mount the Mac OS partition through terminal, it instead tells me that it's a FileVault or Fusion Drive - it's neither, to the best of my knowledge - and that it must be unlocked prior to mounting. So, U found the logical volume and unlocked it using diskutil corestorage command that actually unlocked volumes, and then it ended up as /dev/disk16, and I was still unable to mount /dev/disk0s2, or disk16. Trying to remove the empty Windows partition through DiskUtility results in failure because it's locked. Any and all help is greatly appreciated, as I desperately need this computer for study, and losing files on it is a non-option.
This means that the Mac can't find a valid startup folder to boot from.

The solution to this is to reinstall OS X – power up your Mac while holding down Cmd-R, then select Reinstall OS X (or Utilities -> Reinstall OS X). 
Depending on what version of Mac OS X, you will want to select "Archive and Install" if you want to preserve your files. Follow the onscreen prompts to reinstall Mac OS X.

If you have a backup disk for your Mac, that's a bonus just in case the installation goes wrong.