Im stuck in a black hole!

given R (A,B,C,D,E,F)

and F:

1. A--> BC
2. B--> A
3. C --> D
4. AE --> F

compute {B,E}+ to prove that BE --> DF

My Ans: {B,E}+  = {B,E}+        using 1.


                            = {A,B,E}+    using 2.

                            = {A,B,E}+    using 3

                            = {A,B,E,F}   using 4.

thus, BE =/= DF

but if u start at 2. u get a different answer {ABCDEF}, which proves the above.

Am I missing something? I think my logicis badly wrong.

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