Heather,
The conditionals in this stimulus require very careful attention, but if you diagram them one step at a time, everything will fall into place.
The stimulus essentially says that one conditional is equivalent to the other; it claims that the conditional after the colon means the same thing as the conditional before it, which is supposed to make explicit the absurdity of the first conditional. Since we are meant to parallel the reasoning in this question, we want to know whether the two are equivalent conditionals, because otherwise there may be a flaw (which, of course, we would want to parallel if it exists!).
So, first:
not(government supports)
not(government allows)
This is the first conditional.
The conditional after the colon uses the word "without", which is a necessary condition indicator. Thus, the necessary condition of this conditional is "government subsidy." But because "without" is a word that, like "unless", requires special treatment when identifying the sufficient and necessary conditions of a conditional, we need to employ the Unless Equation to get the sufficient condition.
As I said, "government subsidy" is the necessary condition. The other condition
must first be negated before it becomes the sufficient condition. Thus, the sufficient condition here is "allowed to create art," because the "no" is negated, and the double negations cancel out. Thus, the conditional after the colon is as follows:
allowed to create art
government subsidy
Since "subsidy" and "support" are synonymous in any relevant way in this stimulus, the second conditional is merely the contrapositive of the first.
This is why answer choice (A) is correct - as you identified, the second part of that answer is the contrapositive of the first, as it should be.
Answer choice (B) is a Mistaken Negation, as you also identified.
For answer choice (C), the sufficient condition is "supported by a government grant." Remember that when a statement says "Every member of group A has quality B," the conditional is A
B. Here, it says that being a scientist supported by a grant is sufficient to make success necessary. So:
supported by grant
successful
For the second part of answer choice (C), "without" again requires the use of the Unless Equation. So, "No A without B" = A
B. (B is necessary, "No A" must be negated to become sufficient, so "No-no-A = A by double negation) Thus:
successful
grant
which you can see is not the contrapositive.
In answer choice (D), the first conditional is as in answer choice (C), while the second says that no scientist lacking something (thus, no scientist who does not have support) will be successful. Thus:
not(support)
not(successful)
This is also not the contrapositive of the first conditional.
In answer choice (E), the second conditional mentions being "allowed" to do research, while the first conditional mentions success and support. Thus, the second conditional brings up a third condition that was not in the sufficient or necessary condition of the first conditional. This does not parallel the reasoning in the stimulus, so answer choice (E) is wrong.
If anything continues to be unclear, please let me know!
Robert Carroll