• General advice

make sure to be absolutely clear about the difference between a sufficient and a necessary condition from “A Short Lesson”, and the ways that can be used to express those conditions (e.g., “if…then…” vs. “only if…”, etc.)

  • Question 1

Please do read “X implies Y” as saying “X is a sufficient condition for Y”. I’ve included a clarificatory note. Big hint: Please revise what it means for something to be a necessary condition for something else. Another big hint–this is actually meant to be a simpler question than many of you seem to be taking it. Everything you need is already in the question itself!

  • Question 3

Small clarificatory note added for Dave’s statement. When we say that “given P, Q, R, it can still be X”, we are basically saying that {P, Q, R} does not rule out X.