Consider a simple checkpointing protocol and the following set of operations in the log.

(start, $$T4$$); (write, $$T4, y, 2, 3$$); (start, $$T1$$); (commit, $$T4$$); (write, $$T1, z, 5, 7$$);
(checkpoint);
(start, $$T2$$); (write, $$T2, x, 1, 9$$); (commit, $$T2$$); (start, $$T3$$), (write, $$T3, z, 7, 2$$);

If a crash happens now and the system tries to recovver using both undo and redo operations, what are the contents of the undo list and the redo list?

Consider two relations $${R_1}\left( {A,B} \right)$$ with the tuples $$(1,5), (3,7)$$ and $${R_2}\left( {A,C} \right) = \left( {1,7} \right),\left( {4,9} \right).$$
Assume that $$R(A,B,C)$$ is the full natural outer join of $${R_1}$$ and $${R_2}$$. Consider the following tuples of the form $$(A,B,C): a = (1,5,null),$$ $$b = (1,null,7),$$ $$c = (3, null, 9),$$ $$d = (4,7,null),$$ $$e = (1,5,7),$$ $$f = (3,7,null),$$ $$g = (4,null,9).$$ Which one of the following statements is correct?

With reference to the B⁺ tree index of order 1 shown below, the minimum number of nodes (including the Root node) that must be fetched in order to satisfy the following query: “Get all records with a search key greater than or equal to 7 and less than 15” is _________

The number of min-terms after minimizing the following Boolean expression is _______________ . $$$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$$