Find all the candidate keys of the relational table R

Find the candidate keys of the given relation schema / Find keys of relational table / Which of the following is(are) the candidate key(s) for the relation R?

Question:

5. Given the following relation R and the set of functional dependencies S that hold on R, which of the following options shows the valid candidate keys for R. R(A, B, C, D, E, F) S: {DF → C, BC → F, E → A, ABC → E}

(a) ABC, DEF
(b) ABD, BDE
(c) ABCD, BDEF
(d) DEF, ACD, BCF

Answer:

(c) ABCD, BDEF


Refer the closure finding algorithm here. result := ABCD
result := ABCDE through the functional dependency ABC → E
result := ABCDEF through BC → F
Finally, result := R.
Hence, ABCD is one of the candidate keys.

result := BDEF
result := BCDEF through the functional dependency DF → C
result := ABCDEF through E → A
Finally, result := R
Hence, BDEF is one of the candidate keys.

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Given the functional dependencies, find the candidate keys

Which of the following is the correct set of candidate keys for relation R.

Finding all valid candidate keys of a relational table R