Diagramming Backwards, How Do I Fix?

[whoonfirst]

I am diagraming these conditions backwards and need help understanding the thought process behind the correct diagram.

For instance, problem 1. "The budget will be approved only if the amendment is withdrawn and there is a compromise on education."

My mind sees: The correct answer is:
if AW and CoE ---> BA BA ---> AW and CoE
No BA ---> No AW or No CoE. No AW or No CoE ---> No BA


I had the same problem with #4, # 8, #9, #10. Can someone help me get my brain thinking about and translating this correctly?

[Jonathan Evans]

Hey Who On First!

I hope you're not trying to get me to do a Costello impersonation!

Conditionals are a tough nut to crack, but you're right to ask about how to get to thinking about translating these correctly.

Let's take a step back for a second just to remind ourselves what conditionals are. They're not magic. They're just a way to represent symbolically a certain kind of relationship, the relationship between necessary and sufficient conditions.

Before you can have much luck symbolizing conditionals, you must have a solid grasp of these concepts. Simply memorizing indicator words or rules will help you along, but without an understanding of the fundamentals, you will quickly hit a ceiling.

I always start with the necessary condition, the truth of which is required for something else to be true. In other words, if the necessary condition is not met, the other thing can't happen. Ask yourself what is required. In the example you cite from the LR Bible, what has to happen? Well, the amendment must be withdrawn and there must be a compromise on education spending. These are the necessary conditions. They occur on the right hand side of the arrow.

Now ask yourself what by itself guarantees the truth of something else? The budget approval. This guarantees that we must have a withdrawn amendment and a compromise.

If we don't have a withdrawn amendment, BOOM, no budget approval.

If we don't have a compromise on education, no budget approval.

That's everything right there. Just talk yourself through it.

BA AW & CoE
~AW or ~CoE ~BA

I hope this helps.

[whoonfirst]

Jonathan,

Thank you for taking the time to help me. That makes since, but may I take a little bit more of your time to go over problem 9 on page 209?

Unless they find an eyewitness (EW) and put the defendant on the stand (DoS), they will lose the case (LC).

I diagramed it like this:
LC ----> ~EW and ~DoS
EW or DoS ----> ~LC
I read this as: they will LC if they do not find EW and DoS, but if they do find EW or DoS then they will not LC.

The correct answer is the reverse:
~LC ----> EW and DoS
~EW or ~DoS ----> LC
To me this reads: They will not LC if they find EW and DoS, but if they do not find EW or DoS then they will LC.

Using your advice: I see finding EW and DoS have to happen in order to not LC but please help my potato head figure out the difference. I thought I was saying the same thing - only getting the wrong answer.

[Emily Haney-Caron]

Hi whoonfirst,

Getting the hang of these ideas is definitely tricky! But you're asking the right questions.

I often find it helpful to put it in "if/then" language, making sure I keep the meaning the same. You may want to try that, or may want to focus on identifying which is the sufficient condition (goes before the arrow) and which is necessary (goes after the arrow).

Here, the if/then statement matching 9 would be:
"If they did not lose the case, then they must have found an eyewitness and put the defendant on the stand."

What you put is a mistaken negation; you had the terms on the right side, but you switched around which were negative. That actually flips the meaning by flipping the sufficient and necessary conditions, even though the side stayed the same.

Does that make sense?

[whoonfirst]

Thank you! I'll keep working on it. I have a few months before the exam and want to be prepared.