Remember that 'only if' introduces a necessary condition. So, our necessary condition here is the electorate being moral and intelligent.
If we left intelligent under sufficient, our sufficient condition would then have to encompass both the electorate being intelligent and a democracy functioning well, which are two separate things.
When you have two descriptors attached by 'and' or 'or', keep them under the same condition. When you write the contrapositive, 'and' becomes 'or' and 'or' becomes 'and.'
So, for this example:
A democracy will function well only if the electorate is [both] moral and intelligent.
DFW - > E M and I
It is necessary for the electorate to be both moral and intelligent for a democracy to function well. Therefore, if the electorate is not moral or not intelligent, then a democracy will not function well. This is our contrapositive statement.
E not M or not I - > not DFW
Hope this helps! Please let us know if you have any further questions.
nimakian801on October 22, 2019
I'm actually more confused on how we were able to select the answer choice that had and in it and not or.
Skylaron November 7, 2019
@nimakian Happy to help!
We diagrammed the passage to get: DFW -> M and I The contrapositive of this is: not M or not I -> not DFW
Therefore, "not M" is alone sufficient in the contrapositive to invoke "not DFW." Similarly, "not I" is sufficient to invoke "not DWF." Both do not need to coexist. You can think of this as a two-part diagram: not M -> not DFW not I -> not DFW
Answer choice (C) is diagrammed as: not M and I -> not DFW. Since we have "not M," we can invoke "not DWF." It does not matter if we have "I" or "not I," so (C) is correct and the presence of the word "and" does not alter the outcome.
Does this help? Let us know if you have additional questions!
