Let R=(A,B,C,E) be a relational schema and the set of MVDs and FDs be D={BC→→AE, A→→E, E→→ABC}.
Decompose R into 4NF.
How should I make of this D different decompositions of R?
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Right now you are just asking for us to rewrite a textbook/manual with a bespoke tutorial & do your (home)work & you have shown no research or other effort. Dumps of requirements are not on-topic questions. Please see [ask], hits googling 'stackexchange homework' & the voting arrow mouseover texts. Quote & use definitions, show all steps of your work following your textbook & ask 1 specific question re the first place you are stuck. – philipxy Jan 16 '20 at 00:46
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"I have these FDs & MVDs" doesn't make sense. "These are all the ones that hold"?--Not possible. "These are all the non-trivial ones that hold"?--Not possible. "These are some that hold"?--Question can't be answered. Find out what a *cover* is & what the exact conditions are to apply a particular definition/rule/algorithm. To determine CKs & NFs we must be given dependencies that form a cover. Sometimes a minimal/irreducible cover. And the set of all attributes must given. [See this answer.](https://stackoverflow.com/a/53386492/3404097) – philipxy Jan 16 '20 at 00:50