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Unless the file is erased securely then it possible to "undelete" using third party tools.
 
I just wanted to ask when moving items to trash and deleting does it go from your Mac book air ?

You didn't mention which MacBook Air you have but those machines have SSDs rather than spinning hard drives. With TRIM turned on, once a file is deleted it is very difficult to "undelete" it. Not impossible I'm told, but it requires special processes.
 
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