When someone is “lax,” he or she is “loose” with discipline or care. The word is related to “relax.” In the case of “lax,” it is often implied that such “laxity” is a bad character trait for which the person should be judged negatively. Since “negligence” is the failure to perform a necessary or required task with appropriate care, it is a relative synonym for lax. “Malaise” is the state of feeling uneasy, though one cannot exactly explain why this is the case. Thus, the best synonymous answer for this analogy is “uneasiness.”

Perhaps you have heard the expression, “political consensus.” It is used to describe the situation when a group of differing political parties are able to come together in agreement on some topic. The word “consensus” literally means “feeling or sensing together.” (The “con-” prefix means “with,” as in “congregate” and “chili con carne”—chili with meat). Thus, “consensus” is relatively synonymous with “agreement.” Among the options provided for freedom, several might tempt you because of indirect references and relations (like “fighter,” “constitution,” and “political”); however, the best option is “liberty,” which is the only option that is directly synonymous with “freedom.”

A glutton is a person who does not control the amount of food that he or she eats, overindulging. Such a person can be called “intemperate.” Although it is usually used to describe the forgoing of alcohol, the word “temperance” also can mean self-control regarding desires more generally considered. An imbecile is a foolish or stupid person. Such a person could be called “unintelligent.”

Something that is tedious is repetitive and boring. Tedium describes the state of being tedious, as when we say, “The class was complete tedium, for the professor lectured about the most obvious facts in the world.” Such things are dull and uninteresting; therefore, the analogy could be rewritten, “Just as a state of tedium is dull, so too is something wondrous X.” Something wondrous might be unknown, but even very familiar things can evoke wonder. In a sense, things that are wondrous can be said to evoke a kind of excitement. Thus “exciting” is at least the most acceptable among the answers provided.

"Overjoyed" and "gleeful" are synonyms; therefore a similar word for "miserable" is "gloomy."

"Prudent" means the same thing as "cautious," just as "traitorous" and "backstabbing" are synonyms.

"Luxurious" and "opulent" mean roughly the same thing, just as "dilapidated" and "crumbling" are synonyms.

"Valiant" is another word for "brave," much like "craven" is a synonym for "cowardly."

Something arcane is mysterious and secret, generally unknown by many people. Sometimes, the word is used to describe things that are magical, as in “arcane arts.” It can be used more generally, as in, “For many people, the invisible life of computer programs and circuits appears to be a form of knowledge too arcane to be understood by the uninitiated.” Thus, the analogy could be written, “As something that is arcane is fairly called unknown, so is something fashionable fairly called X.” While something fashionable can be expensive or costly, being fashionable is essentially a matter of being popular. This is the best option among those provided. (Note that this is an analogy of loose synonymy).

Something macabre is unsettling because of its dark correlation to matters pertaining to death. Such a thing could also be said to be “morbid,” which can mean “disturbingly related to or interested in things like death.” Thus, the analogy could be written, “As macabre things are characterized by being morbid, so is something courteous characterized by being X.” Someone who is courteous is well mannered and polite, the latter of which is an option among the answers.