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$2.$ We have the schema R $=($A$,$ B$,$ C$,$ D$,$ E$)$ with the following set F of functional dependencies. F $=\{$ CD $->$ E$,$ BD $->$ AC$,$ C $->$ A $\}$

$1)$ What is $($or are$)$ a candidate key $($or candidate keys$)?($Explain how to compute it or them$)$

$2)$ R is in BCNF$?($Yes or No$),$ and Why?

$3)$ If R is not in BCNF$,$ give a lossless$-$join decomposition into BCNF of schema R$.($Show details$)$