Hello,
Would you please explain the explanation?
I understand how DsB>C can work, but I dont understand how BsD works also. How doe we use BsD without breaking the rule that the arrow must point away from the some statement? I know they are the same thing too, but I am failing to see how we can put them together legally (haha).
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In short, they both work because "some" statements are reversible.
We are start with the following: P: B -> C P: ? C: C - some - D
Our first step should be to make any deductions we can from the given statements (i.e. to find the contrapositives or reverses). Doing so gives us: P: B -> C not C -> not B P: ? C: C - some - D D - some - C
Now, we need to connect the first premise to the conclusion. We can do this with the following premise: P: B -> C not C -> not B P: D - some - B B - some - D C: C - some - D D - some - C
As you noted, "D - some - B" allows us to make the larger chain of "D - some - B -> C" which is simplified into "D - some - C." We can reverse this statement to get "C - some - D," which is our original conclusion.
We could start with "B - some - D" by reversing it to "D - some - B" and following the above steps.
The key takeaway here is that the sentence "D - some - B" is equal in meaning to "B - some - D" because "some" statements are reversible. The same is true of "C - some - D" and "D - some - C." You can think of this in a similar way to how we think of contrapositives having the same logical meaning.
Does that make sense? Please let us know if you have any additional questions and best of luck with your studies!
