lnm87 wrote:
eakabuah wrote:
The right answer is option B.
This is a very good question to firm up one's understanding of conditional reasoning.
The following conditional diagram can be drawn from the information above.
No Rezoning----->Band Together
No Band Together-----> Rezoning
Rezoning---->Sewer System Built
Sewer System not Built ---->No Rezoning
Sewer System Built ----->New Apartments Built
New Apartments not built---->Sewer System not built
New Apartments built---->New Residents
No new Residents--->New Apartments not built
Increased Population---->Overcrowding in Sch and on Roads & New Sch and Roads
No overcrowding in Scho and on roads & New sch and roads---->No increased Pop.
New Rds and Sch----->substantial Tax increase
No substantial Tax---->no new Rds and Sch
New Devt---->Rural Atmosphere Destroyed
Rural Atmosphere not Destroyed--->New Devt
We can form the chain below from the above diagrams:
Not Band Together--->Rezoning--->Build Sewer System--->New Apartments Built--->New Residents--->Overcrowding in Sch, Rds hence new Sch and Rds--->Substantial Tax Increase
Now let's look at the answer choices.
A. Band Together--->New Apartments Not built. False-negative. Incorrect inference.
B. New Apartments Built--->Taxes Increase. A correct inference as can be seen from the chain.
C. No rezoning--->Rural Atmosphere Not destroyed. False-negative. Incorrect inference.
D. New Apartments not Built--->No tax increase. False-negative. Incorrect inference.
E. New Apartments not Built--->No overcrowding in sch and on rds. False-negative. Incorrect inference.
Hence the answer is B.
Hi
eakabuahI have gone through your explanation. I might be asking a silly question but by false-negative is it meant that only the immediate chain element is concluded or vice-a-versa.
Can you help.
Not a silly question at all
lnm87For any given conditional relationship, lets say B is the necessary condition and A is the sufficient condition.
so the diagram for the relationship between A and B is:
A---->B.
we can form three other logical relation from the above information. Two are wrong and the other is right. The right logical deduction from the diagram above is called contrapositive. It simply means, reverse the relationship and negate the conditions.
The contrapositive for A---->B is not B----->not A. A---->B means that if A occurs, then B must have occurred. So if B has not occurred, then we can say that A has not occurred either; this is the contrapositive.
False negative:
not A---->not B. This is not a valid logical deduction. The fact that when A occurs then B must have occurred does not mean that when A does not occur then B did not occur either.
False reversal:
B----->A. This is also not a valid logical deduction from A---->B. The fact that the occurrence of A means that B must have occurred does not mean that when B occurred then A must also have occurred.
Let me simplify the concept of the logic chain by using letters. If we have the following conditional statements,
A---->B
B---->C
C---->D
D---->E
E---->F
we can form the chain below from the conditional statement above.
A---->B----->C----->D----->E----->F
Along the chain, I can deduce that
A--->B, A---->C, A----->D, A---->E, and A----->F
B--->C, B---->D, B---->E, and B----->F
C--->D, C---->E, and C----->F.
D--->E and D---->F.
All of the above inferences are valid since they follow along the logic chain.
The moment you reverse order without negating the conditional terms, then you have a false reversals. For example E----->B, F---->A, D---->C are all false reversals of the valid conditional relationship established in the chain.
Likewise, falsely negation occurs when any of the following inferences are made from the chain: not A---->not B, not A--->not C, not A---->not D, etc.
When you now take these into consideration, you will realize that all the options for the question falsely negated the relationships in the logic chain except option B, which has a valid inference.
I hope I have somehow cleared your doubts to some extent. You can refer to
powerscore CR bible for more detailed explanation on conditional reasoning.