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(fileutils.info)Conditional Executability

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Conditional Executability
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   There is one more special type of symbolic permission: if you use
`X' instead of `x', execute permission is affected only if the file
already had execute permission or is a directory.  It affects
directories' execute permission even if they did not initially have any
execute permissions set.

   For example, this mode:

     a+X

gives all users permission to execute files (or search directories) if
anyone could before.