Grouping Setup Practice Drill #6

[srcline@noctrl.edu]

Hello,

I am not understanding this game at all. I am not seeing the inferences and linkage with rules 1+ 3 and 1+4. Can someone please draw these out for me, because when I am doing it out I am only see the arrow going in one direction.

Also I am confused on when to draw out and use the contrapostives. When I was first doing this problem I drew out all of the applicable contrapostives 2,3,4,5). I am really confused on this promblem, I do not understand the linkages and inferences between the rules.

Thankyou
Sarah

[Dave Killoran]

Hi Sarah,

Thanks for the questions! Let me start by talking about the contrapositive first. The goal is ultimately for you to see contrapositives in an automatic, near-instant manner. It should eventually be the case where when you see a statement like A B, in your mind you not only see that, but the contrapositive (B A) as well. This is because when you have a conditional statement, there is always a contrapositive (CP). So, seeing a statement and its CP should go hand-in-hand. Now, do you need to write out each CP also? My answer is no. I only write out unusual contrapositives. the rule of thumb should be to write it out when you feel that doing so will help you. So, statements like A B aren't going to cause me to write out the CP. Something like A + B C or D would cause me to write it out. I know from the other question you posted that contrapositives are giving you some trouble, so this is a point I really want to make sure you are comfortable with, because it will help eliminate a set of problems you have. So, let me know if the above makes sense, and do not hesitate at all to ask me questions about ti if something isn't entirely clear there

Ok, that said, let's move on to the two inferences you asked about:

• The inference resulting from the combination of rules 1 + 3
  
  Rule #1: B D
  
  Rule #3: C D
  
  Since D is common to both rules, we can combine them into a chain: C D B (B D is reversible, so I can flip it around and it works exactly the same). This "X Y Z" form is a classic inference-generating form, and always results in an inference where the two terms at the ends of the chain cannot go together, which in this specific case is C B. Why does this happen? It's discussed on pages 244-245, and page 264. The gist is that C requires D, but D doesn't like B. So, whenever you have C you must have D, but that knocks out B. The result is that C and B can never go together.
  
  
  The inference resulting from the combination of 1 + 4
  
  Rule #1: B D
  
  Rule #4: G B
  
  This is the same basic inference as 1+3 above, so I'll use the same basic analysis: since B is common to both rules, we can combine them into a chain: G B D. This results in an inference where the two terms at the ends of the chain cannot go together: G D. The gist is that G requires B, but B doesn't like D. So, whenever you have G you must have B, but that knocks out D. The result is that G and D can never go together.

Please let me know if that helps. Both of your inference questions come from the same exact form, and its a form you see a lot on the LSAT. It's also one of the two most frequently appearing inference chains (the other is A B C), so we want to make sure you have this one locked down because you'll see it again. And again. And again Thanks!

[Statiix]

I understand everything about this question and how it's inferences are made however I am having trouble actually combining these rules in a timely manner. When I am combining them, it also feels very dirty as if I am just randomly trying to put things together - it doesn't feel clean or process-oriented. How can I trust myself to combine rules together on a hard question? Is it just practice? Again, is it just practice that's needed?

Is this a good process? What would you do differently? I am trying to get -0 on this section so feel free to critique it heavily.

1) Write down all the rules as they are stated in the question.

2) Re-format rules if necessary and combine obvious ones.
- For example, B --> not D becomes B <---|--> D and B
- For example, B --> G and G --> B become B <--> G

3) Go through the rules by "applying" the first rule to all the rest. Applying means seeing if you can combine them.
- For example, apply rule 1 to 2. Cannot be combined? No? Okay then apply rule 1 to rule 3. Then rule 1 to rule 4. Etc.

4) Now try applying the combined rules from step 3 to the original rules and see if anything happens.

5) Move on to the questions.

[Jeremy Press]

Hi Statiix,

The process you've described is very clean and logical! It will ensure you don't miss anything in terms of connections. To get faster does require practice (for example, recognizing double arrows and double-not arrows immediately will help your "step 2" feel much easier and faster, but that can only happen by seeing lots of games with those rules in them).

If you want to make the process you described more efficient, you can start combining some of the steps as you go. Rather than just writing down the rules, then reformatting them, try to challenge yourself to immediate "translate" the rule into its ideal reformatted diagram. Rather than going through the rules one by one at the end of listing them, try to notice where common variables show up in a new rule you're diagramming and a rule you've already diagrammed in your list. Check right then and there whether there is a combination between those rules you can automatically put into your inference list. By combining steps in this way, you'll be catching important inferences, but you'll be doing it as quickly as possible with a minimum of rereading. This level of efficiency definitely requires practice to implement (and to implement accurately!). Go back through exercises like this one and see how you could've applied the above procedure to arrive at the best diagram more quickly. As you force yourself to do it on scenarios you're familiar with, it will become doable on scenarios you're not familiar with.

I hope this helps!

Jeremy

[Justin.kolesar]

Hello,

I have an additional follow up question in regards to this practice drill. I understand how to identify the inferences from rules 1+ 3 and 1+4. However, I'm not understanding how rules 5 and 6 combine. Can you help me understand? Thanks!

Rule 5: Not H ---> L
Rule 6: M <---|---> L
combined: Not H ---> L <---|---> M

[Justin.kolesar]

Hello,

I have an additional follow up question in regards to this practice drill. I understand how to identify the inferences from rules 1+ 3 and 1+4. However, I'm not understanding how rules 5 and 6 combine. Can you help me understand? Thanks!

Rule 5: Not H ---> L
Rule 6: M <---|---> L
combined: Not H ---> L <---|---> M

I now realize that I wrote the rule M <---|---> L down incorrectly as M---> L and that was were my confusion was stemming from. Sorry!