Solution verification for functional dependency using armstrong axioms

I have the following functional dependencies which includes all attributes of the relation: {AB -> C, BC -> AD, D -> E, CF -> B} CF supposedly is a candidate key. The task is: Show that CF is a candidate key given the functional dependencies listed ACF -> AB (Augmentation) AB -> C (Follows directly form functional dependencies) BC -> BAD (Augmentation) BC -> D (Decomposition) D -> E (Follows directly from functional dependencies) This came up as part of an algorithm, which has no name in my script. In line 10 the candidate key {CF} was discovered and I wanted to verify that it is indeed a candidate key. 1. LEFT = {F} 2. NOWHERE = {} 3. MIXED = {ABCD} 4. RIGHT = {E} 5. 2^MIXED = {{}, {A}, {B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}} 6. LEFT ∪ NOWHERE = {F} 7. {F}G+ (Closure) = {F} 2^MIXED = {{A}, {B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}} 8. {AF}G+ = {AF} 2^MIXED = {{B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}} 9. {BF}G+ = {BF} 2 MIXED = {{C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}} 10. {CF}G+ = {CFBADE} Candidate key! 2 MIXED = {{D}, {AB}, {AD}, {BD}, {ABD}} 11. {DF}G+ = {DFE} 2 MIXED = {{AB}, {AD}, {BD}, {ABD}} 12. {ABF}G+ = {ABFCDE} Candidate key! 2 MIXED = {{AD}, {BD}} 13. {ADF}G+ = {ADFE} 2 MIXED = {{BD}} 14. {BDF}G+ = {BDFE} 2 MIXED = {} I also have no idea why the author choose the description 2^mixed for the combinations of all the attributes