Using two relations R and S $,$ with the join condition Ri$=$Sj$,$ and given the

following information: $($Show all your work$)$

M pages in R with pR tuples per page

N pages in S with pS tuples per page

R contains:

$900$ pages

$30$ tuples per page

S contains:

$1000$ pages

$10$ tuples per page

Buffer size is $102($inclusive of $2$ additional buffers$)$

$($a$)$ Compute the I$/$O cost for R and S using a block nested loop join for both:

R$|><mi>|</mi>$S

S$|><mi>|</mi>$R

$($b$)$ Compute the I$/$O cost for R and S using a hash join.