I think about sufficiency vs necessity as a requirement. In the provided example, students cited as "late" are required to be 5+ minutes late (sufficient). Whereas, if you are 5+ minutes late, you are not required to be cited as "late" (necessary) but you might be!

Example:

They are Senators only if they are Congresspeople.

Senators are "required" to be Congresspeople [sufficient], but Congresspeople are not "required" to be Senators [necessary] (they could be House Representatives).

For sure, and famously Bertrand Russel discovered a paradox in this (which was resolved by a new rule for sets). Basically "Russel's paradox" explains how a set cannot contain itself. An example I pulled off the internet: "Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself."

Sorry probably not helpful for the LSAT but I think it's really interesting. There is a great video by Jeffrey Kaplan (a philosophy professor) on YouTube who extrapolates his own set-based paradox by using predicates of all things!

I find these grammar sections tedious and ultimately unmotivating. At one level I recognize that increasing grammar competency can in turn increase reading comprehension. That said, I also recognize that without intensive studying of thinking about grammar like this, the grammar comprehension won't occur naturally (and more importantly) fast enough. Importantly, though, I don't think intensive studying of grammar is effective when there is so much more else to study. So, at some level I feel reading difficult material more often and training your mind into a state of active reading is more effective than trying to consciously breakdown sentence structure until it becomes subconscious. I'd appreciate feedback on if anyone else feels similarly.

I would say it depends. Naturally, if the argument sufficiently counters the concession, then it strengthens because it has discredited some reference point. Contrarily, if a concession is brought up but the argument fails to address it or makes a weak counter than it hurts the argument. That said, the intention (successful or not) of a concession is often to strengthen the argument or why else would the author add it? Though other times it really is just contextual information, as an argument needs to be staged in the context of prevailing or existing understandings. Now how much this matters for the LSAT and what is more typical for the LSAT is an insight someone else might need to provide. I will say I think it is safe to assume if an LSAT RC passage is using a concession to strengthen its argument, it is most likely going to do it successfully considering the source material is often highly credible.

Example of a concession weakening a theoretical argument:

(Concession) While the Senator from Wyoming is correct that school lunches are underfunded and unhealthy, (premise) he is known to lie and (conclusion) therefore we shouldn't listen to him about increasing funding.

This example has a weak argument, and as a result the concession is actually more compelling when put next to the argument.

Example of a concession strengthening:

(Concession) While the Senator from Wyoming is correct that school lunches are underfunded and unhealthy, (premise) studies show that more funding would not make the lunches healthier and (conclusion) therefore to make the lunches healthier we should think of better solutions than more funding.

By disconnecting the implied causal relationship posited by the Senator this argument successfully uses the concession as a springboard.

Obviously, these examples make no sense (being underfunded is defined by criteria like not being healthy enough) but that is not germane to what I am trying to demonstrate. I am terrible at thinking of examples, but I hope that helps.

I think it's fundamentally something related to how fleshed out the argument is. That is to say, if an argument is more fleshed out it relies on less assumptions (what I would consider unstated and implicit premises that are presumed true without being stated). The Disney example requires less assumptions by the reader to reach the conclusion. Contrarily, the Tiger argument relies on more assumptions (albeit very reasonable, nearly indisputable ones) to reach the conclusion. Seeing the next video in the syllabus seems to confirm this to me.