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Following!

You can attack the significance of the premise or the relevance of the premise; you just can't attack the truth of the premise. If the passage says the study found X, then the study found X. The premise is true, period. But you can still weaken it by saying that the sample was too small to be reliable.

Yes, to be not denied (in the context of the passage) can be interpreted as having received. Note that they are not the same concept, but as mentioned in the explanation, are good enough representations of each other.

Premise 1: If an oral myth is to survive, then it needs to be written down.

(survive → written)

Premise 2: If it was to be written, then it must contain some truth.

(written → truth)

Chaining these up: survive → written → truth

Premise 3: Iliad has survived to this day.

Conclusion(s):

-It being part of the survived-subset of premise 1, means it has membership in the written-superset.

-It being in the written-set, means it has membership in the truth-superset of Premise 2.

Therefore, we can conclude that: The Iliad must have been written down. The Iliad had some truths that was valuable for future generations.

The statement that he can make heroin only if he synthesizes LSD implies that synthesizing LSD is a necessary condition for making heroin. Given that he synthesizes LSD, it follows that he has the capability to make heroin. However, it's important to note that this doesn't necessarily mean he is currently making heroin, only that he can. There may be other conditions that relating to its sufficiency that cannot be concluded.

-"Only" can be used as an indicator word for necessity.

Outside of the context of indicator words, if the condition (synthesizing LSD) is not met, then the consequent action (making heroin) cannot occur. That is not to say that it is the only condition that must be met, but rather, it is required that it happen for the production of heroin - hence, making it the necessary condition.

The lessons mention over- and underinclusion of indicator words, so personally, I try not to rely on it too much and rather focus on training my intuition of necessity and sufficiency.

Take the example we learned a couple of lessons ago. Let's focus on that to start, without worrying about Lawgic.

Cats and mammals are two different concepts. To be a cat, it is REQUIRED that it be a mammal. A cat cannot exist without having fur, warm blood, or lactation capabilities. As such, being a mammal is NECESSARY to be a cat. As such, if you know something is a cat, that's just enough information (SUFFICIENT) to know that it's a mammal. Intuitively, this makes sense (I hope).

If you have that spark of intuition for something, try to articulate it like I did in the previous example. It's a bit harder for more abstract/modified concepts, but you'll eventually get it down.

Hope that helps.

I think, as explained in the lesson, that either one could be a necessary condition, as the contrapositive to it retains its truth either way.

For example, if you have the conditional statement: "Unless it has been raining, then the ground will not be wet," the potential (translated) statements are:

"If the ground is not wet, then it has not been raining." OR "If it has been raining, the ground will have been wet."

Neither negate each other's nor the example's truthfulness.

We're divorcing the argument made from the object clause, and then smushing it back together. Think of it like a conversation.

The claim is (which is the comparative statement): humans act selfishly MORE than they do not act selfishly.

The response: "Well...we don't know that BECAUSE there's no statistical evidence.

There is little to support the conclusion that humans act selfishly (more than they don't), BUT it still wins within the claim itself.

It seems as if our traditional understanding of predicate nouns is not necessarily sufficient for the structure of a 'kernel'. I find if you watch JY's videos on this from CC-v1, it makes for a slightly better understanding.

Per your question, note that the words "are," and "is" are tenses of the verb "to be." Protected, while not technically a noun, is more like a concept (see the lesson note on what we're constituting as a noun in this context). Something being in a national park is a part of the sum of the whole of what is protected.

It may help to rephrase the passage to make sense of the argument.

Tax on sugar-laden foods is now implemented at a level such that it costs a company more to pay the tax than it would have cost to create healthier options. [This is background info]. Implicitly, this means that a company that ONLY makes sugary food will lose money.

[As a result] companies that might produce such foods will now shift towards healthier alternatives BECAUSE companies aim to maximize their profits.

There are a couple of assumptions (listed below) being made in the passage's argument (recall previous lessons), which I suspect may be where you're coming from.

-The only aim of a company is to maximize their profits

-The only way these food production companies can maximize their profits is to shift to healthier alternatives

...and so on.

I think for the purposes of brevity, it was lumped together by the system - I would have considered it a second premise supporting the conclusion of the municipality being bound to react. Might help if one rephrases the passage:

The municipal body is bound to react BECAUSE the public's complaint's about the public transport systems have eroded confidence in such systems AND these systems are vital to urban lifestyle.