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functional-dependencies

Armstrong Axioms - functional dependencies

I need to solve the following past paper question but I can't seem to understand it.

Question

Solution

  • To paraphrase what you have been given:

     A -> B and B -> C still hold

    you are asked:

    Show that A -> B,C is true

    Since A -> B and B -> C (given above), then because of the transitivity rule we can say

     A -> C

    Now working backwards from the decomposition rule we can say that because

     A -> B
 A -> C

 then...

 A -> B,C

    and there you go.