Armstrong Axioms - functional dependencies

Question

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

Answer 1

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.