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Consider following set of FDs on R(A,B,C,D,E,F)

A $\rightarrow$ BCD

B $\rightarrow$ DE

B $\rightarrow$ D

D $\rightarrow$ A

Compute the canonical cover.

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A $\rightarrow$ BCD ( A $\rightarrow$ B ,A $\rightarrow$ C, A $\rightarrow$ D)

B $\rightarrow$ DE  (B $\rightarrow$ D, B $\rightarrow$ E)

B $\rightarrow$ D

D $\rightarrow$ A

Here A $\rightarrow$ D can be reached by ( A $\rightarrow$ B and B $\rightarrow$ D) so this can be removed.

B $\rightarrow$ D can be removed.

So resultant cononical cover is

A $\rightarrow$ BC

B $\rightarrow$ DE

D $\rightarrow$ A
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