Conditional rule in rule testing type questions

currentlystudying

Hey 7sagers,

When I have a conditional rule, do I have to test the conditional rule AND it's contrapositive in the rule testing type questions (the ones that frequently occur as the first question in each game)? Experience tells me the answer is no but I'm not sure why. Could someone explain?

akistotle

Sorry I'm not sure if I understand your question. Could you elaborate on what you mean? Do you have any examples?

paulmv.benthem

@currentlystudying said:
Hey 7sagers,

When I have a conditional rule, do I have to test the conditional rule AND it's contrapositive in the rule testing type questions (the ones that frequently occur as the first question in each game)? Experience tells me the answer is no but I'm not sure why. Could someone explain?

I believe you're referring to what J.Y. often calls a "standard acceptable situation" question, correct?

If I have you right, in the absence of time constraints, yes, you'd be wanting to consider the application of each rule's contrapositive when you're working through the questions. However, translating out each conditional into the contrapositive would be quite time consuming, and I suspect this would cause a significant hit to your score.

Ideally, you want to have a strong intuitive sense of when the conditions for each game are either fulfilled or fail. I don't mean "intutitive" as in naturally or it's something people are born with, but you should spend plenty of time familiarizing yourself with the logic of conditional statements so that when you work through the conditions, you can tell whether a condition has been met or whether it has been failed without translating out a contrapositive.

To illustrate, suppose you have an in-out game with the condition O ---> P. The contrapositive of this condition would be /P --> /O. But, it would take me quite a while (and clutter up my page) if I was to translate this contrapositive for each rule. So, what I want to do instead is realize the logic of what's contained in this statement. More specifically, I want to recognize that If I have an O, then I must have a P. If I do not have the P, then I should not see an O. So, when you have your "standard acceptable situation" question, you want to not only think about whether the sufficient condition is met, but you also want to consider whether the necessary condition has failed. If the latter has occurred, then you should not see the sufficient condition. This allows you to, essentially, accommodate for the contrapositive without spending additional time and energy approaching them as two conditions.

Hope that helps! If not, I"m happy to clarify.