You can think about it a bit like the NY -> USA example.

In this case, it would be, NY -> USA.

K(USA) does not guarantee that K(NY). However, K(NY) guarantees that K(USA).

It might be confusing to continue to use the terminology but if you want me to use it

Being in NY is sufficient to being in the USA. Being in the USA is necessary to be in New York.

To apply to this example. Being "cited 'late'" is sufficient to being 5 or more minutes past the homeroom bell. However, being 5 or more minutes late is NECESSARY but NOT SUFFICIENT to being "cited 'late'".

I hope that helped.

This would just be a difference in active vs passive voice. The subject and predicate would stay the same but it would be considered a more roundabout way to say teh same thing.

I think one of your best options would be to follow-up with them with something friendly while still emphasizing the importance of the LOR. I understand that it may be difficult to foster a relationship with your professors through online classes but I am sure that they still have your best interest in mind. With the academic year beginning to wind up in many states, professors tend to be a bit busier as they are preparing their kids (if they have any) and themselves to return to school/work, respectively.

I would attempt to send a simple follow-up today saying something along the lines of, "Good morning/afternoon Professor/Dr./Mr./Mrs./Ms. _____, I understand that the school year beginning is riddled with moments of high stress and I just wanted to ensure that my email did not get lost in the abyss of ___ ____ __-."

Then, wait about a week or so (depending on when your LOR deadline is) and send another follow-up email, this time being a bit more pressing. "Good morning/afternoon......

I just wanted to follow up and check on the status of the LOR. If you are no longer willing to complete it or foresee there being a logistics/time issue, please let me know so that I may seek a LOR from another professor. ___________________ (- this is where you emphasize how important it is to you and that you do not mind asking another professor for help because you need this to be the best possible and as soon as possible.(/p)

If the professor that you are trying to get a LOR for is world-renowned or great in their field or you just REALLY like them, it may be best to attempt to schedule an office hours in person and make the trip out there.

Hope this helps!

Simply, yes. However, there are many different ways that this question could be later posed. Something that helps me is to think about the perceived conclusion, "All libraries and bookstores are intellectual places..." and look at the other statements and see if there is any relationship between them. Both of the statements that follow do not mention the level of organization in either of the institutions, so you could deduce that it is not an argument. It could be that you used your previously-held knowledge of knowing that bookstores and libraries have a lot of books to determine that it was an argument. I would recommend just ignoring your previously-held knowledge when looking at foundations exercises. Good luck!