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### PowerScore LGB Workbook Help

Posted: Thu Nov 15, 2012 6:08 pm
I'm working on some drills from the PowerScore Logic Games Bible workbook. This seems like a great book. I plan on posting questions I have from this book in this thread. Others using this book should feel free to chime in and post questions, also.

I came across a diagramming issue in the first chapter. How would I diagram the following: "If Greta does not speak at the fundraiser, Harrison speaks at the fundraiser" (pp. 4).

According to the explanations, this would "produce a double not-arrow where both terms are negated (the polar opposite of the rule represented here):" (pp. 32)

G <---l---> H

I don't understand what they mean in the explanation. Here's my guess:

~G <---l---> ~H

Is this right?

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 9:13 am
Yes.

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 9:37 am
Actually that is a common mistake. This is known as a negative sufficient condition. It would be diagrammed as follows: If G is not selected then H is, or if /G -> H. The contra positive would be if /H -> G. In essence, if H isnt selected, G is. And if G isn't selected, H is. However, unlike a double not arrow, both CAN be selected at the same time. This is in pg 200 of the bible, btw.

If it was written as If G is selected, then H is not, then it would be a double negative arrow. The difference is with double not arrows, you can have one or neither, but not both. With negative sufficient, you can have one or both, but not neither.

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 9:43 am
Typhoon24 wrote:Actually that is a common mistake. This is known as a negative sufficient condition. It would be diagrammed as follows: If G is not selected then H is, or if /G -> H. The contra positive would be if /H -> G. In essence, if H isnt selected, G is. And if G isn't selected, H is. However, unlike a double not arrow, both CAN be selected at the same time. This is in pg 200 of the bible, btw.

If it was written as If G is selected, then H is not, then it would be a double negative arrow. The difference is with double not arrows, you can have one or neither, but not both. With negative sufficient, you can have one or both, but not neither.

lsataddict did it correctly. That's how to use a double not symbol to diagram that relationship. Your way is correct as well, if you want to use two separate diagrams to do so.

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 10:03 am
I'm a little confused, Grond. OP's and my answers directly contradict each other. Either one is right or neither (THAT would be proper use of the double not arrow lol). I submit that the double not arrow may not be used in this situation because it states that both can not be present. However, I believe they can both be selected.

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 10:10 am
You're correct Typhoon, it only says if one is NOT selected then you know the other IS selected. If one or the other is selected you cannot draw any information about the other variable from this information.

### Re: PowerScore LGB Workbook Help

Posted: Fri Nov 16, 2012 10:12 am
Typhoon24 wrote:I'm a little confused, Grond. OP's and my answers directly contradict each other. Either one is right or neither (THAT would be proper use of the double not arrow lol). I submit that the double not arrow may not be used in this situation because it states that both can not be present. However, I believe they can both be selected.

Look at his diagram. He has "not G" and "not H" at the ends of the double not arrow, thus correctly showing that G and H cannot both be out of the group. Your confusion is probably due to the fact that most games rules that involve a double not involve two variables that cannot both be in the group. The double not can be used in both circumstances: both cannot be in the group (at least one out), and both cannot be out (at least one in.)