Given Relation:
R (A, B, C, D, E, F, G, H)
Given Functional Dependencies (F):
AB → C
A → DE
B → F
F→ GH
Attributes A and B are not present on the right side of any Functional Dependency(FD). Hence, AB must be present in the candidate key and super key.
Let's find the closure of AB.
{AB}+
= {AB} (axiom of reflexivity)
= {ABC} (AB → C, given FD)
= {ABCDE} (A → DE, given FD)
= {ABCDEF} (B → F, given FD)
= {ABCDEFGH} (F → GH, given FD)
The closure of AB is:
{AB}+ = {ABCDEFGH}
This means AB can determine all other attributes of the relation R. Hence, {AB} is a Super Key for the relation R.
Besides {AB}, all the possible combinations of {AB} with other attributes are also Super Keys.
For example,
{ABCD}
{ABF}
{ABE}
{ABFG}
etc. are also Super Keys.