@cpie15 Z ==> X is NOT the same thing as not Z ==> not X.
This is commonly referred to as an improper negation (i.e. don't just negate!).
Remember, from every general we can create the contrapositive, which is identical in meaning, by reversing AND negating.
Let use an example to make this clear as clear as possible.
We know that all carrots are vegetables.
C ==> V
However, it would not be proper to conclude that something is not a vegetable simply from the fact that it is not a carrot.
What if it was lettuce? Celery?
What we could state with 100% certainty, however, is that if it is not a vegetable, it cannot be a carrot.
This is the contrapositive, which again is created by reversing AND negating.
not V ==> not C
Hope this helps!
For a more in-depth review of these concepts, please watch our video lesson on Sufficient & Necessary conditions.
lilyweilingyeMarch 5, 2019
I also thought it was Z - >X. My thought process was:
If all Z are X (Z->X) And Some X are Y (X-some-Y) Then some Z must be Y (Z-some-Y)
Can you please explain why this is wrong?
RaviMarch 11, 2019
Hey there,
Happy to help. Let's take a look at why this is wrong.
Let's look at your example.
If all Zs are Xs (Z - >X), then we could have 100 total Zs, and all 100 would be Xs. However, what if there are a million Xs? This would mean that 1 in 10,000 Xs is a Z.
If some Xs are Ys, what if there is only 1 X that is also a Y? This is possible. Additionally, what if this 1 X that's also a Y happens to be one of the 999,900 Xs that isn't a Z? This would be fine too, and in this scenario, there could be ZERO overlap between Zs and Ys.
Let's look at what's given in the stimulus.
P: X-some-Y
P: ?
C: Z-some-Y
If we add X - >Z (not Z - >not X), then the argument would work.
If all Xs are Zs, then we could have 100 Xs in total and all of them would be Zs. Let's say we have a million Zs.
We also know that some Xs are Ys. Let's say 1 X is a Y.
The conclusion that some Zs are Ys has to follow because all Xs are Zs, and there is 1 X in our example that's also a Y, so there is overlap between Y and Z. Therefore, Z-some-Y.
You were really close, but you just got the missing premise reversed. Instead of Z - >X, the correct answer is X - >Z (not Z - >not X). Do you see why now based on the explanation above? Let us know if you have any more questions!
