Given R $=($A$,$ B$,$ C$,$ D$,$ E$)$ and functional dependencies AB $->$ C$,$ E $->$ A$,$ C $->$ DEB, give candidate key$($s$)$ for R$.$ Show how you reached closure on each candidate key. Find all $3$ candidate keys.

Given the relation r$($E$,$F$,$G$,$H$,$I,J$)$ and the functional dependencies GI $->$ EF and E $->$ H and I$->$ J$,$ give a lossless decomposition of r into BCNF$.$ Your answer should list the normalized relations that you will create in place of r$($E$,$F$,$G$,$H$,$I,J$).$ New relations should be stated in the form of r$($x$,$y$,$z$),$ with the primary keys underlined.