You would need to look at the food and city together. In this puzzle, 12:30 is either Ollie or (the set of people that are possible for *either* oyster *or* Naperville). Look down the left-hand side of the grid at the rows for Naperville and oyster simultaneously. If you could find someone who was Xed out on both oyster/Naperville, you could go ahead and X that person out on the 12:30 line, too (except for Ollie, who in this case is the only one).
I can't remember what the set notation looks like, it's been too long since I had those math classes
But I'm fairly certain this would work. eta - because it would read as [Person] is neither oyster nor Naperville, and they are obviously not Ollie, so they can't be 12:30.