$1.$ Consider a relation R with five attributes ABCDE. You are given the following dependencies: A $->$ D; DE $->$ C; CB $->$ A$.$

$1.$ For each FD $X $\backslash$rightarrow Y$$,$ compute the closure $X$^+$$

$2.$ List all keys in R$.$

$3.$ Is R in $3$NF$?$ Explain.

$4.$ Is R in BCNF$?$ Explain.