A question in Set Dependency prof

Dear All,

I am trying to find a mathematic prof for the following question and i also would like to know what do you call this problems in mathematic term so that i could find the right materials in web.

The question(Thinking)

you have the table that consist of severals attributes a1,a2,a3,a4,...,am with numbers of rows Rn. There is a dependency between attributes. For example, a1 -> a3 (as postcode -> suburb). Similarly, a2->a4 (job titles->income).

The thing that i would like to know is it true to say

if

a1->a3 and a2->a4

then

{a1,a2}->{a3,a4}

I also appreciate if you could recommend some web site that discuss this concept.

Thank you very much in advance for your assistant.(Wink)