Candidate Keys / Reduction

Question

I have a relation

R = (S, T, U, V, W, X, Y, Z) which has the FD's

TW -> Y
TW -> Z
Y -> X
Y -> S
V -> U
X -> T

I'm trying to find the candidate key for R but because of the relationship

TW -> Y -> X -> T

I can't figure out what it is. I know it has to have 'V' and 'W' in it but I don't know if I should also have 'X' or 'T'.

Answer 1

The candidate key of this relation R is TWV and XWV both because they cannot be derived from one another. so this relation has two candidate keys and it is possible for aa relation to have more than two candidate keys.

Answer 2

You say that W is dead sure inside any candidate key.

Therefore,

TW -> Y -> X -> T

becomes

T -> Y -> X -> T

So, which one do you choose, X or T ?

And why not Y ?