In the War and Peace passage, choose the correct word to complete the clause "the members of which are _____ against the background of Russian social life during the war against Napoleon".

Introduction / Context:
The focus now is on how the characters of the novel are presented within their social environment. The sentence reads the members of which are blank against the blank background of Russian social life during the war against Napoleon. We must choose the verb that correctly describes how characters appear or are shown in a literary work. The question tests understanding of a common term used for depiction in art and literature.

Given Data / Assumptions:

• The subject is the members of five aristocratic families.
• The phrase involves a background of Russian social life.
• Options are portrayed, displayed, treated, based, arranged.
• We need a verb that matches background and fits literary description.

Concept / Approach:
In artistic and literary language, portrayed against the background of is a very familiar expression. It means the characters are depicted with a certain social or historical setting behind them, much as figures are shown against a painted background. We need a verb that fits this metaphor. The strategy is to test how each option combines with against the background of and whether it yields a natural, standard phrase in critical writing.

Step-by-Step Solution:
Step 1: Try displayed against the background of. This phrase might be used for physical objects in an exhibition but is not typical for characters in a novel. Step 2: Try treated against the background of. Treated against is not a normal combination for literary analysis. Step 3: Try based against the background of. We normally say based on, not based against, so this fails grammatically. Step 4: Try arranged against the background of. This is more suitable for visual composition in art but is not the conventional critical verb for character depiction. Step 5: Try portrayed against the background of. This is a standard expression in literary and art commentary. Step 6: Conclude that portrayed is the only fully correct and idiomatic choice.

Verification / Alternative check:
A quick mental scan of common phrases confirms this: Characters are portrayed against a backdrop of war and poverty or The hero is portrayed against the background of industrial England. Such sentences are very common in study guides and reviews. None of the other verbs is used in this structure in formal English discussion of fiction. Therefore, portrayed against the background of Russian social life is the logically and stylistically correct version.

Why Other Options Are Wrong:
Displayed: Suggests putting something on show like a product or picture, which makes the narrative style sound mechanical. Treated: Used in the sense of dealt with, but treated against the background is not standard usage. Based: Always takes on rather than against in this context, so it is grammatically incorrect. Arranged: Might be used for staging actors in a theatre but does not have the established critical meaning that portrayed has. Thus, these options either break collocation rules or fail to capture the nuance of depiction in fiction.

Common Pitfalls:
Students sometimes rely on rough meaning and pick displayed or arranged because they imagine a visual scene. However, in formal literary English, portrayed is the normal verb for describing how characters are shown within a setting. Learning a few such set expressions helps greatly in cloze tests that are based on standard examination passages.

Final Answer:
The correct word is portrayed, giving the phrase the members of which are portrayed against the background of Russian social life during the war against Napoleon.