Just wanted to say the visual example was super effective, thank you for that! I've been trying to make visuals for a lot of the more complicated topics we've covered and used a similar beaker analogy for sufficiency/necessity. I'd love for more lessons to include visual comparisons like these!

For Question #2, why must it be /B -> R and not B -> /R? "Joffrey must kill Bran or Robb" doesn't indicate a negated condition, so I'm confused why we would jump to "NOT killing Bran means he kills Robb" and not "killing Bran means he doesn't kill Robb." Struggling a lot with identifying sufficient and necessary conditions in such a short phrase.

for anyone who doesn't know, in the blind review page there's a super helpful but easy-to-miss feature called the "wrong answer journal" that asks you 1) why the right answer is right, 2) why the wrong answer is wrong, and 3) how you can improve moving forward. i've been filling it out for all the drills i get wrong and my wrong answer journal for the "extrasensory perception" question was INCREDIBLY useful, i got a 5/5 on max difficulty because of it. would absolutely recommend it as a part of ur study method

general question, also taking into account a bunch of the other comments i've seen people leave below: what grammatical purpose does the word "by" serve? i understand why "winds" is not the object in #4, because the hurricanes aren't triggering the winds, but i'm wondering if "by" could also demarcate the presence of an object in other instances and what that would look like