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Yes, but that is not the only property used.
This illustrates the associative property.
Yes, but it would be a pointless thing to do. The associative property is much more appropriate.
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. Assuming that you mean d~(e~f) = (d~e)~f where ~ is a binary operation, it is the associative property.
The exact answer will depend on the details of the prism which is not shown!