. Suppose we have a relation R (x ,y ,z), where the pair of attributes x and y together form the key. Attribute x ranges from 1 to 100, and y ranges from 1 to 1000. For each x there are records with 100 different values of y, and for each y there are records with 10 different values of x. Note that there are thus 10,000 records in R. We wish to use a multiple-key index that will help us to answer queries of the form: SELECT z FROM R WHERE x = C AND y = D; where C and D are constants. Assume that blocks can hold ten key-pointer pairs, and we wish to create dense indexes at each level, perhaps with sparse higher-level indexes above them, so that each index starts from a single block. Also assume that initially all index and data blocks are on disk. a) How many disk I/O ’s are necessary to answer a query of the above form if the first index is on x? b) How many disk I/O ’s are necessary to answer a query of the above form if the first index is on y? c) Suppose you were allowed to buffer 11 blocks in memory at all times. Which blocks would you choose, and would you make x or y the first index, if you wanted to minimize the number of additional disk I/O ’s needed?