Problem $2$

Consider a relation R with five attributes ABCDE.

$2.$ If each instance for R listed above is legal, what can you say about the FD A $->$ B$?$

$1.$ For each of the following instances of R$,$ state whether it violates $($a$)$ the FD BC $->$ D and $($b$)$ the MVD BC $-$ D:

$($a$)\{\}($i$.$e$.,$ empty relation$)$

$($b$)\{($a$,2,3,4,5),(2,$ a$,3,5,5)\}$

$($c$)\{$a$,2,3,4,5),(2,$a$,3,5,5),($a$,2,3,4,6)\}$

$($d$)\{$a$,2,3,1,5),(2,$a$,3,4,5),($a$,2,3,6,5)\}$

$($e$)\{($a$,2,3,4,5),(2,$a$,3,7,5),($a$,2,3,4,6)\}|.$

$(1)\{$a$,2,3,4,5),(2,$ a$,3,4,5),($a$,2,3,6,5),($a$,2,3,6,6\}$

$($g$)\{$a$,2,3,4,5),($a$,2,3,6,5),($a$,2,3,6,6),($a$,2,3,4,6)\}$