Only if the electorate is moral and intelligent will a democracy function well.
The stimulus gives us a conditional rule: only if the electorate is moral and intelligent will a democracy function well. The "only if" marks a necessary condition, so we can write this out as:
function well → moral AND intelligent
The question asks us what we can logically infer from the stimulus. Since we just have one conditional statement, let's make sure we understand it and its contrapositive. Again, the statement translates to:
function well → moral AND intelligent
By the contrapositive: /moral OR /intelligent → /function well
So we know that if we see any well-functioning democracy, the electorate must be both moral and intelligent. And if the electorate is either not moral or not intelligent (or both), then a democracy won't function well.
Which one of the following ███ ██ █████████ ████████ ████ ███ █████ ██████
If the electorate ██ █████ ███ ████████████ ████ █ █████████ ████ ████████ █████
Incorrect. This translates to:
moral AND intelligent → function well
This confuses the sufficient and necessary conditions from the rule given in the stimulus.
Either a democracy ████ ███ ████████ ████ ██ ████ ███ ██████████ ██ ███ █████ ██ ███ ████████████
This answer choice says that either a democracy does not function well — or else the electorate is not moral or not intelligent. You can read the "or else" as meaning "if not": so if a democracy does not not function well, i.e., if a democracy functions well, then the electorate is not moral or not intelligent.
In other words, the second half of this statement translates to:
function well → /moral OR /intelligent
This directly contradicts the rule given in the stimulus.
If the electorate ██ ███ █████ ██ ███ ████████████ ████ █ █████████ ████ ███ ████████ █████
Correct. This translates to:
/moral OR /intelligent → /function well
This is just the contrapositive of the rule in the stimulus, so it is a valid inference.
If a democracy ████ ███ ████████ █████ ████ ███ ██████████ ██ ███ █████ ██ ███ ████████████
Incorrect. This translates to:
/function well → /moral OR /intelligent
This switches around the sufficient and necessary conditions from the contrapositive of the stimulus's rule.
It cannot, at ███ ████ █████ ██ ████ ████ ███ ██████████ ██ █████ ███ ███████████ ███ ████ █ █████████ ████ ███ ████████ █████
Incorrect. What this answer choice is saying is that whenever the electorate is moral and intelligent, then a democracy must function well:
moral AND intelligent → function well
This flips around the sufficient and necessary conditions from the rule given in the stimulus.
More intuitively, realize that we don't know that having a moral and intelligent electorate guarantees a well-functioning democracy. We just know that it is necessary for a well-functioning democracy — but there could be other conditions that need to be met that we don't know about. So for all we know, it's perfectly possible to have an electorate that is moral and intelligent and still have a democracy that doesn't function well.
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