Now, let's add on to the first example above (mentioning D, E, and F) to include a 4th variable, G.
Evidence: D ---> E
Evidence: G -> NOT E
Conclusion: D ---> NOT F
We can take the contrapositive of the second piece of evidence to give us "E -> NOT G"
Then, we can link the two pieces of evidence together to give us:
Evidence: D -> E -> NOT G
Conclusion: D -> NOT F
Just like before, since the sufficient conditions are the same, we can link the necessary conditions to give us:
Sufficient Assumption #1: NOT G ---> NOT F
Sufficient Assumption #2: F ---> G
Just like before, we link the parts that are different, going clockwise (in this case, the necessary conditions).
***
Now, here's an example based on a real LSAT PrepTest question:
Suppose we have an argument where the evidence is:
Evidence: C -> NOT T
Evidence: P -> T
Conclusion: P ---> NOT H
Again, we can take the contrapositive of the evidence, then link it to the other piece of evidence to form a longer chain:
Evidence: P -> T -> NOT C
Conclusion: P ---> NOT H
The middle piece of evidence about "T" is irrelevant.
We can link NOT C to NOT H forming the (sufficient assumption) conditional statement:
Sufficient Assumption: NOT C ---> NOT H
This conditional, when combined with the evidence, forms a longer chain guaranteeing our conclusion.
Same thing works if we have the contrapositive:
Evidence: C -> NOT T -> NOT P
Conclusion: H ---> NOT P
Again, the middle piece of evidence about "T" is irrelevant.
We can link H to C forming the (sufficient assumption) conditional statement:
Sufficient Assumption: H ---> C
This conditional, when combined with the evidence, forms a longer chain guaranteeing our conclusion.
Here's the answer choices for this one, diagrammed:
(a) H -> T
(b) H -> C(c) T -> P
(d) H -> NOT C
(e) C -> NOT P
We see that choice B (H -> C) is exactly what we predict based on our formula.
Cool, huh?
More fun LSAT goodies coming your way soon.
-LSAT Steve
P.S. By the way, for those who have it, this example is based on an actual LSAT question: PrepTest 35 = October 2001 LSAT, Section 1, Question 22, p226 in Next 10.
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2. Logical Reasoning Explanations
The explanations that should have come with the LSAT. These don't just fall back on "out of scope," but actually tell you why the wrong answers are wrong, why the right answers are right, and the easiest way to get the correct answer.
3. Logical Reasoning Cheat Sheet
Based on what I'd typically do in college: read what the professor emphasized and condense it all onto a single piece of paper. It gave me a quick reference, making things a lot less threatening and a lot more manageable.
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