Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements. $S_1$ : Read misses in a write through L1 cache do not result in writebacks of dirty lines to the L2. $S_2$ : Write allocate policy $\textit{must}$ be used in conjunction with write through caches and no-write allocate policy is used with writeback caches. Which of the following statements is correct?

To determine the correctness of each statement:

1. Statement $S_1$: In a write-through L1 cache, every write to L1 is immediately propagated to L2. As a result, the data in L1 is always consistent with the data in L2, and lines in L1 never become "dirty" (no dirty bit is required). Therefore, when an eviction occurs due to a read miss (or any miss), no dirty line writeback to L2 is ever needed. Hence, $S_1$ is true [2].

2. Statement $S_2$: Typically, the write-allocate policy is used with write-back caches (so subsequent writes to the allocated block can be handled quickly in the cache), whereas no-write allocate is commonly paired with write-through caches [2]. Furthermore, these policies are not strictly mandatory together, and $S_2$ incorrectly swaps their standard associations while asserting that write-allocate *must* be paired with write-through. Hence, $S_2$ is false.

Therefore, $S_1$ is true and $S_2$ is false, which corresponds to Option (A).