basically, the idea is that negating the sufficient condition doesn't tell us anything about the necessary condition

remember, sufficient -> necessary; just like how cat -> mammal (if you are a cat, then you are a mammal-- but just because you are a mammal, doesn't necessary mean you are a cat- you could be a dog)

so when we say, like in the example you're referring to, that W → /S → /Q, that means that W and /S are the sufficient condition and /Q is the necessary condition

so if we "fail" (negate) the necessary condition here, /Q, we get Q

the sufficient conditions are affected by this change, because now we have to negate those too because they fall under the Q bubble (they come before Q in the chain)

so we basically negate the whole chain before /Q, and it becomes Q → S → /W

but what about R?

we know that the full chain is W → /S → /Q → R, but R comes after /Q in the chain

this is because for R, /Q is the sufficient, and R is the necessary condition

so now, even if we "fail" (negate) /Q, it's not going to affect R at all- because R is the necessary condition

all we know is that R is adopted-- whether Q is adopted or not will not affect that

but if R was NOT adopted, we know that would affect whether Q is adopted or not, because Q will not be adopted ONLY IF R is adopted

an easy way to think about this is basically: sufficient comes before necessary in a chain; X can impact the stuff before X, but X cannot impact the stuff that comes after it

took me a little bit to figure this out, because the kumar example confused me inititally, so I wanna explain in my comment in case it helps anyone else out to think of it like this:

-we just learned the indicators for /necessary/ conditions, so we know that "only if" indicates that "arriving more than 5 min past the bell" is a necessary condition

-we are told that kumar arrived 17 min past the bell, and intuitively we want to assume that he must be late

but remember: sufficient -> necessary

-if i am a cat, that is sufficient to know that i am a mammal. but if i am a mammal, that does not necessarily mean i am a cat.

the same applies to this argument

-if i am late, than it is sufficient to know that i arrived 5+ min past the bell. but arriving 5+ min after the bell does not necessarily mean i am late.

-think about it like this-- kumar arrived 17 min past the bell, but there's many reasons he could possibly not been late: he could have just not gotten caught, or maybe had an excuse so he didn't get written up, etcetc...we don't know!

but from the information we've been told, we aren't able to make the assumption that he's late