what does the phrase "less/more that assumption renders the argument vulnerable to criticism" mean? still kind of confused on that phrase

what's the difference between a necessary and sufficient condition? and does that have anything to do with whether the "symbol" in on the right of left side? it feels late into the syllabus to ask this but I kept getting confused...

could someone please explain 7.1-7.5? why wouldn't a contrapositive be a part of our final answer? also, for some of the other questions, how does the "only if" placement change the way our X -> Y answer would look like?

could someone please explain the "Kumar" example it really confused me

is it beneficial to understand the contrapositive perspective of these questions? or if I were to understand the main english to lawgic translation, that's "good enough"

if I answered #5 as "some" instead of "most did not go home with children" is that considered incorrect?