Also worth mentioning, in C# the OR operator is short-circuiting. In your example, Close seems to be a property, but if it were a method, it's worth noting that:
if (ActionsLogWriter.Close() || ErrorDumpWriter.Close())
is fundamentally different from
if (ErrorDumpWriter.Close() || ActionsLogWriter.Close())
In C#, if the first expression returns true, the second expression will not be evaluated at all. Just be aware of this. It actually works to your advantage most of the time.