Logical syllogism — determine which conclusions follow beyond doubt. Statements: 1) All the locks are keys. 2) All the keys are bats. 3) Some watches are bats. Conclusions: (1) Some bats are locks. (2) Some watches are keys. (3) All the keys are locks.

Introduction / Context: A three-premise syllogism with two universals and one particular checks whether you can keep track of subset chains and avoid invalid converses or unwarranted intersections.

Given Data / Assumptions:

• Locks ⊆ keys.
• Keys ⊆ bats.
• Some watches ⊆ bats.

Concept / Approach: From transitivity, locks ⊆ bats. “Some watches are bats” does not imply anything about keys unless watches are stated to be keys. Converses like “All keys are locks” are not implied.

Step-by-Step Solution: (1) Some bats are locks — since locks ⊆ bats and locks are assumed to exist, there are locks that are bats. Hence true. (2) Some watches are keys — unjustified. While some watches are bats, keys are a subset of bats; the watches could lie outside keys within bats. (3) All the keys are locks — converse of Statement 1; not supported.

Verification / Alternative check: Example: bats = {k1, w1}; keys = {k1}; locks = {k1}; watches = {w1}. Then (1) holds, but (2) and (3) fail.

Why Other Options Are Wrong: Options including (2) assume an overlap not guaranteed; options including (3) assume a converse.

Common Pitfalls: Treating membership in a larger set (bats) as proof of membership in its subset (keys).

Final Answer: Only (1)