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Default IF AND OR functions

I have one cell that has 5 precedents, I can change one precedent using IF
function, however that one precedent can change 20 different ways. I've been
using the IF and AND function in the following way
IF(A1=AA1,BB1)*AND(A2=CC1)...(four more times), AND is a set of conditions
that have to happen for BB1 to formulate.
AA1-AA20, BB1-BB20, CC1-CC20 represent lists used for Data Validation in A1,
A2 and so on. I'm thinking that I would like to write my formula like this:
IF(A1=AA1,BB1)Or if (A1=AA2,BB2)*AND(A2=CC1), but I'm not getting the
results that I'm after. How do I write the formula: IF 'all these conditions
apply' OR IF 'all these conditions apply' THEN fill in the cell.
I hope this isn't hard to understand, sorry if it seem muddy.
Thanks for any help.

Jig
 
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