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No of Candidate key

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Given relation R(A, B, C, D, E) and set of functional dependencies   

F = {AB → C, AB → D, D → A, BC → D, BC → E}

Number of candidate key in the following relation have?
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$B$ cannot be derived using any functional dependency. So, it will necessarily present in candidate key.

$(AB)^+ = \big \{A,B,C,D,E\big \}$

$(BC)^+ = \big \{ B,C,D,E,A \big \}$

$(BD)^+ = \big \{ B,D,A,C,E \big \}$

$(BE)^+ = \big \{B,E \big\}$

So, above relation has $3$ candidate keys $\color{maroon}{\big \{AB,BC,BD \big \}}$

Also the given relation in "3NF"
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