For inclusion to hold between two cache levels L1 and L2

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For inclusion to hold between two cache levels L₁ and L₂ in a multi-level cache hierarchy, which of the following are necessary?
1. L₁ must be a write-through cache.
2. L₂ must be a write-through cache.
3. The associativity of L₂ must be greater than that of L₁ .
4. The L₂ cache must be at least as large as the L₁ cache.

1. 4 only
2. 1 and 4
3. 1, 2 and 4
4. 1, 2, 3 and 4

Correct Option: B

Because inclusion says the L₂ cache should be superset of L₁ cache. If “Write through update” is not used (and “write back update” is used) at L₁ cache, then the modified data in L₁ cache will not be present in L₂ cache for some time unless the block on L₁ cache is replaced by some other block. Hence “write through update” should be used.