Conditional Possibilities Drill #4

[jr3136]

The part that confuses me about this question in is the "could be true" part and how N could occur or not occur. I'm struggling to see the relationship "if O occurs" how N is affected. I ended up with "P or occurs or does not occur, Q occurs or does not occur" but was not sure what would about the relationship with N. Any help would be greatly appreciated!!!!

Thanks!

[Dave Killoran]

Hi JR,

Thanks for the question. This is a pretty tough drill overall, and it really tests if you understand the relationship between a sufficient condition and a necessary condition. That relationship really comes down to this:

• If a sufficient condition occurs, then you know the necessary condition occurs.
  
  If a necessary condition occurs, then all you know is that the sufficient could occur (meaning it might, or it might not).

So, when we come back to #4, once O is established as occurring, two things result:

• Because O is necessary for N, N can occur, or not occur (which is then N).
  
  Because O is sufficient for "P or Q," either P or Q, or both, must occur.

From the looks of it, the P and Q part was no problem for you. So, let me know if the above clears up the N part, and then you should be good to go

Thanks!

[mbrefo]

I have a similar question for Homework, Page 2-59, but for #3 the second half. If the sufficient ensures that the necessary occurs and if the necessary occurs, one is not sure if the sufficient occurs, how can the answer provided for this question be correct?

In number 3, it states if K does not occur what:

I thought it must be true that if L will not occur since the sufficient K is not occurring. However, H or J could not occur is the answer to the must be true question. I'm confused about this answer.

[Steve Stein]

Hi,

That's a good question; what you've asked about is called a Mistaken Reversal. Let's focus on just that part of the diagram: K L

So, if K occurs, L must occur, but if K does not occur, that doesn't tell us anything about L:

K L?

Why is that? let's consider another example: If you have recently won the lottery, you are rich:

recent lottery win rich

So, we know what happens if you win the lottery. But if you haven't recently won the lottery, that doesn't tell us anything about whether or not you are rich.:

recent lottery win ?

(...not having recently won the lottery is not all that telling; there are a lot of rich people who have never played the lottery).

I hope that's helpful! Conditional reasoning can be very challenging, so please let me know whether this is clear--thanks!

~Steve

[mbrefo]

This explanation is very clear and helpful! Thanks so much!