Question 42

The schedule is:

Testing Statement P (Conflict Serializability):
Find all conflicting operations between distinct transactions:

• Variable $Y$: $R_1(Y)$ precedes $W_2(Y) \implies T_1 \to T_2$.
• Variable $X$: $W_1(X)$ precedes $R_3(X) \implies T_1 \to T_3$.
• Variable $Z$: $R_2(Z)$ precedes $W_3(Z) \implies T_2 \to T_3$.
  The edges in the precedence graph are $T_1 \to T_2$, $T_1 \to T_3$, and $T_2 \to T_3$. The graph has no cycles (topological sort order: $T_1, T_2, T_3$). Hence, $S$ is conflict-serializable. Statement $P$ is true.

Testing Statement Q (Recoverability):

• In schedule $S$, transaction $T_3$ reads $X$ after $T_1$ writes $X$ ($W_1(X)$ followed by $R_3(X)$). Thus, $T_3$ reads uncommitted data from $T_1$ (a dirty read dependency).
• In a recoverable schedule, for any transaction $T_j$ that reads a value written by $T_i$, $T_i$ must commit before $T_j$ commits.
• Statement $Q$ states: 'If $T_3$ commits before $T_1$ finishes, then $S$ is recoverable'. If $T_3$ commits before $T_1$ finishes, and then $T_1$ subsequently aborts, $T_3$ has committed using aborted data and cannot be rolled back, making the schedule unrecoverable. Hence, statement $Q$ is false.

Therefore, $P$ is true and $Q$ is false, which matches option B.