do you wear safety goggles in handball?
All the keys are locks. This is part of the original statement so is true. However, it might be held not to follow as the other parts of the syllogism are irrelevant to it. Some bats are locks. This follows from the first two parts (If all locks are keys, and all keys are bats, then some bats must be locks. We can't say all bats are keys because we are not told anything about all bats) Some watches are keys. This does not follow. The watches that are bats may not be the same bats that are keys. They could be different bats altogether. We have no known connection between keys and watches.
You don't need to pruchase any new parts. A knowledgeable locksmith can simply re-key your existing locks. I suggest anyone buying an established home have their locks re-keyed. You just don't know how many keys are floating around. Anyway, I had all my locks re-keyed so that a single key worked for every lock. You could probably even get instructions from the internet/book to do-it-yourself, but a locksmith can do it much quicker. They disassemble the door knob, set the pins to match the key and re-assemble the door knob - finished.