Answer:
The False Dilemma Fallacy.
Explanation:
Logical fallacy is a set of deduction which is taken as invalid or wrong because of a flaw in the logical arrangement of an argument.
The above example comes under the False Dilemma Fallacy of logical fallacy because false dilemma fallacy concludes that are only two possible outcomes in an argument.
It assumes that if one does not support an argument then he/she is against it totally. It does not look for other possibilities or avenues that may be present.
For instance, "if we you don't sign up for this petition then you clearly does not support animal rights" is another example of The False Dilemma Fallacy.
Since an absolute phrase modifies a noun, and is separated from the rest of the sentence using a comma usually, with no conjunctions, the only correct answer here is the first one. Because there is a comma, there is no conjunction like in the third sentence, so it has to be correct.
Honestly I have no idea what your talking about, but id do hope someone will answer your question. I'm sorry