I'm going through the "Skill Builder - Group 2 Translations" unit of the Conditional and Set Logic section in the Core Curriculum and I'm having some trouble understanding why contrapositives were not used for questions 7.1-7.5. Was looking through the forums and comments under that unit and couldn't find much that explained why contrapositives weren't being used here. I did, however, see a comment that mentioned contrapositives not being used because the conditional language was used to express a potential causal relationship (more than a sufficient-necessary relationship). However, it still seems that those statements are conditional with comparative and causal elements (at least based on the explanations provided for those statements and how I and others interpreted them).
So would statements indicating there being causal and/or comparative elements not require contrapositives, especially if the statements can also be translated into lawgic and indicate there being a sufficient/necessary relationship??
My apologies in advanced if this type of question is meant to go under that unit and not in the discussion forum. It's just that there wasn't much of a response (if any) from the tutors about this.
looking back at everyone's comments and i think i have a better grasp of what's being shared in this lesson (please let me know if this is totally off #help):
it wouldn't be valid to infer that kumar would be marked at "late" even though he meets the necessary condition of being over 5 minutes late. why? because the necessary condition does not fill the sufficient condition (i.e. being marked as "late") ... so just because kumar arrived 17 mins after the last ring does not mean he was also marked as late.
that's why when they were comparing "if" and "only if" sentences in "Avoid Confusing Sufficiency for Necessity", it would have made sense for kumar to be marked as late "if" he arrived more than 5 minutes late... because then he would have filled the sufficient condition, whereas he would be marked as late "only if" he was more than 5 minutes late... he is fulfilling the necessary condition, but there is no guarantee that he is part of the subset of students that are also marked as late as a result of arriving 5+ minutes after the last bell.
so it sounds like the sufficient condition provides more of a guarantee that the necessary condition has been filled, while the necessary condition only guarantees that the necessary condition was filled... it doesn't always extend to the sufficient condition.
does that sound right?