$3.$ Consider the database below and answer the questions based on it$.$

Assume you only have a statistical interface, so only aggregate queries will be successful. You know Debbie is a female Computing Lecturer. The questions below explore how we might determine her salary using inference, in the presence of various query size restrictions.

$($a$)$ Assume there is no limit on the query size. Give a sequence of two queries that will identify the salary of Debbie.

$1\mathrm{.}0$ Mark

$($b$)$ Suppose that there is a lower and upper query size limit that satisfies

$\backslash [$

k $\backslash$leq$|$X$($C$)|\backslash$leq N$-$k

$\backslash ]$

with $\backslash ($ k$=2\backslash ).$ Show a sequence of queries that could be used to determine Debbie's salary.

$1\mathrm{.}5$ Mark