Step 1: Understanding the Concept:
This question tests English grammar and vocabulary. We need to select a pair of words that fit grammatically into the blanks and create a logical, meaningful sentence.
Step 2: Analyzing the Sentence Structure:
First Blank: The structure "........... the facts, she proceeded..." suggests a relationship of contrast or opposition. She made her decision \textit{in spite of} the facts. We need a word that conveys this meaning and is grammatically correct when preceding a noun phrase ("the facts").
Second Blank: The structure "...finally ending up with a ........... situation" requires an adjective to describe the outcome of her decision.
Step 3: Evaluating the Options:
(A) Nevertheless, happy: "Nevertheless the facts" is grammatically awkward. "Nevertheless" is an adverb and usually connects two clauses (e.g., "The facts were clear; nevertheless, she proceeded.").
(B) Apparently, initially: "Apparently the facts" is grammatically incorrect. "Initially" describes a starting point, which contradicts "finally ending up".
(C) However, noteworthy: "However the facts" is grammatically incorrect. Like "nevertheless," "however" connects clauses.
(D) Notwithstanding, sad: "Notwithstanding" is a preposition meaning "in spite of," and it fits perfectly before the noun phrase "the facts." The sentence "Notwithstanding the facts, she proceeded with her decision..." is grammatically correct and logical. Ending up in a "sad" situation is a plausible consequence of ignoring facts.
Step 4: Final Answer:
The pair "Notwithstanding, sad" creates a sentence that is both grammatically correct and logically coherent.