Discussion
Assume that each one of the above statements is true. Which of the following must be true if it is also true that no Hatfields ride horses.
*This question is included in Nova Press: Set E - If/Then Logic Practice, question #2
(A) | The only people who can farm are horseback-riding McCoys. |
(B) | ... |
(C) | ... |
(D) | ... |
(E) | ... |
(F) | ... |
The solution is
Posted: 01/04/2012 05:58
All the answers seem to be right, how do I know which one to pick?
Posted: 01/05/2012 00:21
Hey Patrick,
It helps if we diagram these problems, as the logic can be hard to see otherwise.
Here are the diagrams:
Hatfield → can't farm.
McCoy → can farm.
McCoy → not Hatfield
not a Hatfield → horseback rider
Now, let's look at the answer choices:
(A) The only people who can farm are horseback-riding McCoys.
- This won't work. We only know that the Hatfields can't farm, and that the McCoys can. We can't conclude anything about ALL other people, which we'd have to be able to do in order to draw the conclusion in this answer choice.
(B) Anyone who does not belong to the McCoy clan belongs to the Hatfield clan.
- Again, we can't say this is true. What about the Jones family? The Smith family? (The problem here is the "anyone.")
(C) All horseback riders can farm.
- This doesn't make any sense. We know that if you're not a Hatfield, you're a McCoy. And we know that if you're not a Hatfield, you must be a horseback rider. We can't say anything about ALL horseback riders.
(D) All horseback riders must be McCoys.
Again, we can't conclude anything about ALL horseback riders. None of the diagrams above allow us to.
(E) All McCoys are horseback riders.
* This follows directly from our diagram: McCoy → not a Hatfield → horseback rider
Choice (E) is our winner. See why diagramming is useful?
It helps if we diagram these problems, as the logic can be hard to see otherwise.
Here are the diagrams:
Hatfield → can't farm.
McCoy → can farm.
McCoy → not Hatfield
not a Hatfield → horseback rider
Now, let's look at the answer choices:
(A) The only people who can farm are horseback-riding McCoys.
- This won't work. We only know that the Hatfields can't farm, and that the McCoys can. We can't conclude anything about ALL other people, which we'd have to be able to do in order to draw the conclusion in this answer choice.
(B) Anyone who does not belong to the McCoy clan belongs to the Hatfield clan.
- Again, we can't say this is true. What about the Jones family? The Smith family? (The problem here is the "anyone.")
(C) All horseback riders can farm.
- This doesn't make any sense. We know that if you're not a Hatfield, you're a McCoy. And we know that if you're not a Hatfield, you must be a horseback rider. We can't say anything about ALL horseback riders.
(D) All horseback riders must be McCoys.
Again, we can't conclude anything about ALL horseback riders. None of the diagrams above allow us to.
(E) All McCoys are horseback riders.
* This follows directly from our diagram: McCoy → not a Hatfield → horseback rider
Choice (E) is our winner. See why diagramming is useful?
Posted: 01/05/2012 11:31
Thank you so much. I get it. You guys do a great job at this. God bless you