Question $7$ options:

Consider relations R$($a$,$ b$,$ c$),$ S$($a$,$ d$),$ and T$($a$,$ e$,$ f$)$ to be joined on the common attribute a$.$ Assume that there are no indexes available on the tables.

There are B $=445$ pages in the buffer

R spans M $=1,500$ pages with $80$ tuples per page

S spans N $=4,500$ pages with $150$ tuples per page

T spans O $=200$ pages with $250$ tuples per page

In computing the I$/$O cost$,$ you can assume the simplest cost model where pages are read and written one at a time. You can also assume that you will need one buffer block to hold the output block. You may ignore the cost of the writing of the final results.

What is the cost of sorting the tuples in R on attribute a$?$

What is the cost of sorting the tuples in$$S on attribute a$?$

What is the cost of the merge phase in the worst$-$case scenario?

What is the cost of the merge phase assuming there are no duplicates in the join attribute?

Now consider joining R$,$ S and then joining the result with T$.$ Suppose the cost of the final merge phase is $800$ and assume that there are no duplicates in the join attribute. How many pages did the join result of R and S span?