No, Jerry could not drive only on Tuesday and Thursday.
The rule "Jerry drives on Wednesday or Saturday or both, and he may also drive on other days" means that Jerry HAS to drive either in the Wednesday or the Saturday spot, but in addition to holding one of these spots he may also hold the other spot and he may also drive on another day that is not Wednesday or Saturday.
The key word in the rule is "also." Therefore, we write "J -> W or S or both" because we know that J will fill at least one of these spots, in addition to possibly filling more.
Does that make sense? Please reach out with any other questions and best of luck with your studies!