If anyone is a visual learner, this is the best way I helped myself understand.

@Oblivion Thinking about it in terms of nesting dolls could work.

But in your written statement it has to be "some of A is in B, and all of B is in C, therefore some of A is in C."

You can't chain what you wrote: "some of A is in B and some of B is in C"

A <--s--> B, B <--s--> C

cannot become A <--s--> C

@AnthonyFlores Yes the negation of "some" is "none" or "no".

Original statement: Some alphabets are not phonetic. aka 1%-100% of alphabets are not phonetic

A <--s--> /P

Negation: No alphabets are not phonetic. aka 0% of alphabets are not phonetic -- No A are /P

Using "No" as it is a conditional indicator from group 4 where we negate the necessary condition,

A --> P, (All) Alphabets are phonetic.

@Oblivion I think you are confusing that "No A" means /A, which is not the case. "No" is instead a conditional indicator (Group 4) so

For your Q2, "no alphabets are not phonetic" does mean "All alphabets are phonetic".

No A are /P. & "No" is a Group 4 conditional indicator meaning that we negate the necessary and in this case that then makes it: A --> P

@16dnholli Thinking of this like math, you'd think that the slash would distribute, but this isn't math since we're only using arrows and symbols to represent language and short-hand logic.

/P <-s-> /C would mean "Some non-parrots are not clever". This really isn't the opposite of the original statement "Some parrots are clever".

Since "some" means anywhere from 1% to 100% of the parrots are clever, the opposite of a "some" relationship means that we have to be outside those boundaries to negate -- at 0%. So the opposite of "Some parrots are clever" is that "No parrots are clever". And if we make that statement into Lawgic it becomes P-->/C.

@mattiesas the negation of the whole relationship!

Just like how /A meant the negation of a single condition, the parenthesis show that the negation in /(A->B) applies to the whole relationship rather than just one condition.

@Tannercho06897 Contrapositive and negation are different!

Contrapositive is an equivalent way of expressing the relationship. We typically create a contrapositive of a normal conditional relationship (ex. cats are mammals) by flipping sufficient and necessary conditions, and negating each condition (ex. if not a mammal, then not a cat). These are two ways of expressing the same relationship.

Negation of an All statement/relationship ("it is not the case that all ...") is creating the opposite of the relationship. For example, the negation of "all cats are mammals" would be "some cats are not mammals". They express totally different relationships between the sets.

@Valleygirlala I think he means that if an adoption center is not eligible, it could mean any one of three things:

1. it does not have an interactive website (/IW)

2. it is not a 501c (/501c)

3. it does not have either a website and is not a 501c (/IW and /501c)

He is merely reminding us that option 3 is also possible, which is that an ineligible adoption center could lack both a website and not be a 501c.

@MRod I think the reason it is being broken apart is if you are trying to link to another premise such that says "if O happens then ...". Although the new premise doesn't explicitly say anything about N happening, you still know the new conditional relationship is triggered if M happens because M triggers both N and O.

@emill1517 My favorite way to think about unless is this:

"A will occur unless B occurs."

In my head, this means that the only way for A not to happen (/A), is for B to happen. So, if A does not occur, then B did.

Translation: /A --> B

In this example, "There will not be a good show unless there are sophisticated listeners in the audience"

The only way for there to be a good show, is for sophisticated listeners to be in the audience. If there was a good show, then sophisticated listeners were there. Therefore, good show --> sophisticated listeners

@JeffreyRamirez Breaking down question 3.

You've got it nailed for "carry ring -> venture into mordor". Then I think you got caught on the "unless".

"No one can venture into Mordor unless they are brave." Our two clauses are: "no one can venture into Mordor" unless "they are brave"

Unless tells us to choose a clause and negate it. Let's negate the Mordor clause into "one can venture into Mordor". Now putting into the sufficient condition spot: M -> brave

if one can venture into Mordor, then they have to be brave. (sounds like it fits our rule that no one can venture unless they are brave)

your chain then becomes: carry ring -> venture into M -> brave!

@AdrianaMendez "every" is a Group 1 conditional indicator! I would treat "every time" the same as "every" and put it into group one, same as "any" & "anytime" or "when" & "whenever".

But rule of thumb, if you think about it conceptually after getting stuck with indicators;

Which sounds more like the sentence given in the Question 4:

"If Sherlock goes to a crime scene, then he will find clues" or

"If Sherlock finds clues, he is visiting a crime scene"

That always helps me out if I'm stuck on sufficient vs necessary by making clear phrasing. Hint: what if he finds clues elsewhere? like interviewing suspects? going to a crime scene doesn't sound very necessary to his ultra clue finding ability!

@DeborahJimenez If you really wanted ABS to be in your Lawgic translation as a condition (I don't think this is an efficient way of thinking), it should instead look like this:

P1: ABS --> common

P2: /advantages --> /common

Chain from Premises:

ABS --> common --> advantages

Conclusion:

ABS --> advantages

^I prefer the more efficient thinking of ABS as a "dot" in the sets of common traits and confers survival advantage instead of doing the above with ABS in the conditional Lawgic translation as a condition. That said it can be done.

@DeborahJimenez

I think your incorrect mapping probably stemmed from a misidentification of the conclusion. The conclusion is the second sentence of the stimulus: "therefore, ABS confers survival advantages". The conclusion is not the last sentence and the last sentences should be properly interpreted as the main premise:

/survival advantages --> /common

@JeffreyRamirez If you are stuck mixing up the group 1 and 2 indicators, but recognize the conditional relationship, you can always think through it logically by rephrasing!

"It's always sunny in Philadelphia"

Think: Is this saying (1) "if it's sunny, I'm in Philadelphia" or rather (2) "if I'm in Philadelphia, it is sunny".

Thinking through it, this has to be the latter (2). The first doesn't make sense because it could be sunny in other places, not just Philadelphia! The second makes sense as another rephrasing of the sentence because if you're in Philadelphia, it's always sunny! It matches up with the original sentences' concept.

@isabellagirjikian Your example is spot on, but the "is" and "is not required" I think introduces negatives ("not") which might make things confusing. I've thought about this a bit and way I use familiar language to wrap my head around is:

sufficient means "guarantees" and necessary means "required to be eligible" to wrap my head around it most when thinking about what each does and does not prove.

example:

Taking 7Sage guarantees (is sufficient for) taking an LSAT course prep. & not taking 7Sage does not guarantee anything about taking an LSAT course prep.

Taking an LSAT course prep gives you eligibility (is necessary for) to be taking 7Sage. & not taking an LSAT course prep makes you ineligible for taking specified 7Sage.

Question 4 is puzzling me. I thought it would be a trick question. Having "no statistical evidence" does not mean that the statement that follows is true. So we have no way to know if humans acting selfishly is actually a winner in terms of comparing more often. There could be no evidence in the other direction as well! Kinda of like the rules we were following in negative comparative claims. Seems like the answer is just accepting this major flaw that a lack of evidence = something not being true ... (and yes I understand that this exercise is purely about the steps of comparatives but I think this is a poor example choice).

@cworth1512 Hi! I initially thought the same on the A vs B portion. On second read, I think the biggest hint is in the wording "than to" before the mention of most other cultivars of corns. Linguistically, the comparison matches and pits against the wording of "to sorghum". So we're looking at closeness of some cultivars of corn TO sorghum vs TO most other cultivars of corn. It's almost an unsaid reference that the comparison always ties back to "some cultivars of corn" as the subject of our sentence and point of reference. I think using this reasoning at the start of our breakdown of A vs B will help the next two steps follow logically. Hopefully that makes sense!