Relation R with only prime attributes: R in 3NF but may not BCNF
Example:
$R(A,B,C,D,E,F)$
$\left \{ AB\rightarrow C,C\rightarrow D, CD\rightarrow AE,DE\rightarrow F, F\rightarrow B\right \}$
$CK: AB,AF,ADE,C$
$BCNF$ $3NF$
$AB\rightarrow C$ $\checkmark$ $\checkmark$
$C\rightarrow D$ $\checkmark$ $\checkmark$
$CD\rightarrow AE$ $X$ $\checkmark$
$DE\rightarrow F$ $X$ $\checkmark$
$F\rightarrow B$ $X$ $\checkmark$