Consider the table:

A B C $($tuple#$)$

$5525551$

$2555152$

$4515153$

$2555554$

$4515455$

$1545556$

$1545457$

$3535158$

$($a$)$ Which of the following FDs cannot hold, and which may hold in the above table? No expla$-$nations required.

A $->$ B$,$ A $->$ C$,$ B $->$ C$,$ B $->$ A$,$ C $->$ A

$($b$)$ Which of the following are potential candidate keys and which cannot be$?$ No explanations required.

A$,$ B$,$ AB$,$ AC$,$ BC