Reply To: Conditional Statements and Contrapositives (Chapter 13)

July 28, 2016 at 11:39 am #2317

Thank you so much for your reply, LSAT DAN! Yes, the examples definitely do help to clear up some of the confusion with numbers 2 and 4. Independent of the examples though, I’m still having trouble reasoning why the contrapositives of these statements do, in fact, create equal and opposite logical statements. By themselves, the contrapositives of numbers 2 and 4 seem to say something totally different than their original statements.

For number 2, /C –> V; having no C triggers V. So far so good. But to me its equal and opposite /V –> C seems to stand by itself as a different statement altogether. Even though no C ensures V, why does no V then guarantee C? I can use number 4, scenario 2, on page 180 as an example of my confusion: “O will be performed if L is not.” (/L –> O) Not singing L triggers singing O; how can it then be guaranteed that not singing O will guarantee L? In the vacation and car example, you had to choose one, and one would prevent the other. In the singing example though, there are other songs available, and not all songs will even be used. Why is one guaranteed to exist with the other’s absence? If that is a true logical conclusion, is it then also logical to conclude with this conditional statement that either C or V will definitely be included in an in/out ordering game and either C or V will go in each group of a grouping game (ingredient and car service examples)?

Number 4 now makes sense! V must guarantee C, because if we didn’t have C, we couldn’t have V cleared it up for me. Thank you! Like with the first example, it seems to follow that C does not necessarily you’ll have V.

Maybe I’m getting hung up on something that doesn’t much matter (or maybe I’m missing something totally obvious). I’m taking Mr. Kim’s advice seriously though, and want to make sure I fully understand all underlying logic behind a contrapositive before I use the technical “reverse and negate” method. Thanks again for your help!