Two Rule Inference Drill #6

[Guadalupe]

From LSAT Logic Games Bible WORKBOOK (revised 2014)
Drill#6 pg 12
Solutions: pgs 101-102

"Every variable is in in a group, and H cannot be in group 1 unless K is in group 1. J is in group 2 only if L is in group 2."

Rule 1: H(1)----->K(1)
Rule 2: J(2)------>L(2)

"As this is a two-value system game, the contrapositive of any conditional rule typically yields useful information. The contrapositives of the two rules above are as follows:

Contra:
Rule 1:K(2)----->H(2)
Rule 2:L(1)------>J(1)

My question: How do the contra rules work? Unsuccessfully applied Unless Equation and does not translate in my mind because of the second variable group (which I also used as a base).Two groups: 1 and 2 with a vertical setup, three slots each. Note: second variable groups are in parentheses, sorry didn't know how to type out subscripts.
Many many thanks in advance...

[Nikki Siclunov]

Hi Guadalupe,

Thanks for your question. You have represented the rules - and their contrapositives - correctly. To answer your question "how do the contrapositives work?", well - they are logically identical in meaning to the original rules. Take the first rule, for instance. We know that whenever H is in group (1), K must also be in group (1). So, by the contrapositive we know that if K is not in group (1), H cannot be in group (1) either. Since there are only two groups that these variables can be in, the contrapositive yields a positive statement: if K is in group (2), H must be in group (2):

H(1) K (1)
K (2) H (2)

Keep in mind, however, that H and K need not always be in the same group! This must be true only when H is in (1), or else K is in (2). But, if H is in group (2), that tells us nothing about K, which - in that case - could be in either group. To conclude otherwise would be a Mistaken Negation of the original rule (and a Mistaken Reversal of the contrapositive). Likewise, if K is in group (1), it is entirely possible that H is in group (2).

The same analysis applies to the second rule.

If you had trouble with the Unless Equation, read again the chapter on Conditional Reasoning from the Logic Games Bible. Also, you may want to take a look at this blog I wrote awhile back:

http://blog.powerscore.com/lsat/bid/281 ... s-Equation

Last, I'm not quite sure why you put three dashes in each group (1) and (2). Is there a mandate that six variables be divided equally between the two groups? Unless there is a numerical stipulation requiring each group to have a requisite number of variables, I would simply represent groups (1) and (2) as two separate spaces on my page (a single dash, for instance, could represent an entire group).

Hope this helps! Let me know.

Nikki