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Practice Drill in LG Bible Workbook

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I'm really confused by the practice drill that's on page 59 of the latest edition of the workbook (and the explanation is on page 193).

The explanation says Not F :arrow: KJH Block

I get that, but I don't understand the contrapositive. The workbook says that the contrapositive of the inference above is Not H :arrow: F.

I would have said that the contrapositive is Not KJH Block :arrow: F. It seems like a leap to change "Not KJH Block" to simply "Not H."

By the way, was this a real LSAT game or was it made by Powerscore for the sake of creating a practice drill? For some reason, I find it much more challenging than usual.

Thanks in advance!
Jonathan Evans
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Hi, lsat_novice,

This is a PowerScore drill to illustrate different kinds of game mechanics.

Let's look at this conditional rule:


Now let's think about this a slightly different way. This rule means that if F is not selected, then K is selected and J is selected and H is selected:

    F :arrow: K & J & H

To make a contrapositive, you flip the statements and negate each statement. Thus, the contrapositive of the above conditional would be:

    K or J or H :arrow: F

Remember that when you negate "and," it becomes "or."

Next, notice that K, J, and H are each sufficient by themselves to guarantee that F is selected. In other words, if we know K is not selected, then F is selected; if J is not selected, then F is selected; if H is not selected, then F is selected.

    K :arrow: F
    J :arrow: F
    H :arrow: F

This is how we get the contrapositive H :arrow: F.

I hope this helps!
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I was understanding grouping games and the rules really well up until this question and then my confidence was shattered. I was able to write out the main rules and their contrapositives but then got extremely stuck once I had to realize the whole if I then G then F sequence. I basically have zero idea how we even got to the point of making templates and there is no detailed explanation for this. I was soooo stuck on this question. Is there a way to get a more detailed explanation of the entire game?
Jonathan Evans
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Joined: Thu Jun 09, 2016 2:12 pm
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Location: DFW, Texas

Hi, Haychnya!

This is a challenging conditional sequence! The best possible explanation is contained in the Logic Games Workbook on page 193, but we would be happy to address any questions about parts of this game that you find challenging.

Let's step through the G :arrow: F sequence:

  1. Check out the rules that have multiple elements in common. For instance, consider G :arrow: F and G :arrow: J & K.
  2. Take the contrapositive of the first rule. F :arrow: G.
  3. Combine this with the second rule. F :arrow: G :arrow: J & K
  4. Now ask yourself whether any other rules share elements in common with the above chain conditional. Yes, there's also I :dblline: J,K.
  5. Go back to the sufficient condition of the chain in step (3) above, F. F implies J & K & G. We know because J and K are selected there is no I. Thus we know F :arrow: J & K & G & I
  6. In this scenario we have no F and no G and no I. We have J and K, but that's not enough to fill a flowerpot. We need one more, but there's only one option available, H. This is how we arrive at the inference F :arrow: H & J & K.

Don't get discouraged! Step through this methodically. As you read the explanation, write down each of the rules and inferences. See if you can spot their implications. Then move on to the next step. Difficult games such as these might require two or three passes through them fully to grasp the mechanics. If at any point in the explanation, you find yourself confused, stop right there. Work on figuring out the one smaller point you find challenging. Once you have figured that one out, move on to the next step. This process takes time, but fortunately with practice this will become both easier and faster.

Please follow up with more questions about this exercise.