Consider the following partial Schedule S involving two transactions $$T1$$ and $$T2.$$ Only the read and the write operations have been shown. The read operation on data item $$P$$ is denoted by read$$(P)$$ and the write operation on data item $$P$$ is denoted by write $$(P).$$

Suppose that the transaction $$T1$$ fails immediately after time instance $$9.$$ Which one of the following statements is correct?

Consider a B⁺ tree in which the search key is 12 bytes long, block size is 1024 bytes, record pointer is 10 bytes long and block pointer is 8 bytes long. The maximum number of keys that can be accommodated in each non-leaf node of the tree is ____.

Consider the relation $$X\left( {P,Q,R,S,T,U} \right)$$ with the following set of functional dependencies
$$\eqalign{ & F = \left\{ \, \right. \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left\{ {P,R} \right\} \to \left\{ {S,T} \right\}, \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left\{ {P,S,U} \right\} \to \left\{ {Q,R} \right\} \cr & \,\,\,\,\,\,\,\,\,\,\left. \, \right\} \cr} $$
Which of the following is the trivial functional dependency in $${F^ + },$$ where $${F^ + }$$ is closure of $$f$$ ?

Given the function $$F = P′ + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$$ consider the following statements.

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S1} \right)\,\,\,\,F = \sum {\left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S2} \right)\,\,\,\,F = \sum {\left( {0,1,2,3,7} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S3} \right)\,\,\,\,F = \sum {\Pi \left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S4} \right)\,\,\,\,F = \sum {\Pi \left( {0,1,2,3,7} \right)} \cr} $$

Which of the following is true?