Consider a key$-$value database $$ a database that purely stores key$-$value pairs $$ organized with LSM$-$tree on

the disk and the associated structures, a self$-$balanced search tree and a bloom filter, in the main memory.

$($A$)$ When an equality search query q arrives with key w$,$ denote by n $>0$ the total number of SSTable files

that have been dumped from the memory to the disk by the database. Could the total number of SSTable

files the database needs to visit to answer q be $0?$ Please explain your answer. $[3$ marks$]$

$($B$)$ Can a bloom filter create false positives? Please explain your answer. $[3$ marks$]$

$($C$)$ Can a bloom filter create false negatives? Please explain your answer. $[3$ marks$]$