Trivial join dependency

I'm struggling to comprehend how to "operate" with join dependencies, so I have a query that I hope will help me make sense of it all.

Here is a simple brief explanation from Wikipedia:

A table T is subject to a join dependency if T can always be recreated by joining multiple tables each having a subset of the attributes of T.

The definition of a trivial join dependence is as follows:

If one of the tables in the join has all the attributes of table T, the join dependency is called trivial.

Is it feasible that every join dependence of a relation R might be a simple join dependency if we collapse it into a lossless decomposition? Awesome would be one illustration.

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    The answer is yes. Every join dependency of a relation R can be represented as a set of simple join dependencies. A lossless decomposition of R into its component tables is one way of expressing this set of simple join dependencies.

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