There are two examples that quotes the same rule but the card indicates different answers. Can someone explain me why?
1) P: A -> C
P: ?
C: Not C -> D
The answer I found is that “Not A -> D” (Using the contrapositive I found that “Not C -> not A”. Them I applied this rule to the conclusion and found that “Not C -> Not A -> D”, so the premises missing is “Not A -> D”). According to the card, this is the right answer.
2) P: X -> A
P: ?
C: Not A -> B
The answer I found was “Not X -> B” (Using the contrapositive I found that “Not A -> Not X”. Them I applied this rule to the conclusion and found that “Not A -> Not X -> B”, so the premises missing is “Not X -> B”). According to the card, this answer is wrong; the right one would be it’s contrapositive “Not B -> X”.
As you can see, I followed the same logical reasoning for both, however the card indicates different answers. Can someone please explain me why? I can’t understand why I have to use the contrapositive on the Example #2
Also, I can’t understand the following example:
P: X -> Y
P: ?
C: Y exists
According to the card, the correct answer is “X exists”. However, I understood from the lesson that when the sufficient is true/exists I can assume that the necessary is also true/exists, but not the contrary. Why is that the answer?
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To your first question: You did everything right on those missing premise drills. Remember that a contrapositive carries the exact same logic as the original statement, so they are completely interchangeable. This is why we are able to rearrange them as we please on these drills. If you complete one of these questions, but the given answer on the flashcard is the contrapositive of your response, then you can consider it a correct answer. You might want to get in the habit of writing both, but I wouldn't worry about the difference in your two examples. You answered them correctly.
Here is the problem with your second question. You are treating it like a missing conclusion drill, instead of a missing premise drill. Your complaint would be perfectly valid if the setup was this:
P: X ---> Y P: Y exists C: ?
Answer: X exists
This is incorrect! Like you said, we can't go from necessary to sufficient. However, your example asks us to fill in the missing premise.
P: X ---> Y P: ? C: Y exists
Answer: X exists.
There are no problems here. Combining these two premises does yield the correct conclusion.
AnthonyHJune 17, 2020
This explanation was very helpful! I was having the same issue. Thank you.
