In this passage about democracy and dictatorship, choose the preposition that best completes the blank in the clause: “The conditions ______ which democracy can flourish are difficult to define … ”

Introduction / Context:
This cloze question is taken from a passage contrasting democracy with dictatorship. The sentence describes the circumstances in which democracy can grow successfully. You are asked to choose the correct preposition for the phrase “conditions ______ which democracy can flourish”. The answer depends on understanding both grammar and idiomatic usage in English.

Given Data / Assumptions:

1) The sentence fragment is “The conditions ______ which democracy can flourish are difficult to define”.
2) The options are: by, for, under, at.
3) The phrase refers to the circumstances in which a system (democracy) can work well.
4) We want a standard relative construction: “conditions ______ which …”.
5) The rest of the passage talks about democracy being a slow growth and dictators rising to power.

Concept / Approach:
In English, we commonly use “conditions under which” to refer to the circumstances or situation in which something happens or can exist. The preposition “under” is closely associated with “conditions” in this sense. Other prepositions like “by”, “for” or “at” would either change the meaning or make the sentence ungrammatical. We must choose the preposition that fits both idiomatically and grammatically.

Step-by-Step Solution:
Step 1: Recognise that the phrase “conditions … democracy can flourish” describes circumstances, not agency or purpose. Step 2: Recall common collocations: we say “under certain conditions”, “conditions under which something happens”. Step 3: Test “by”: “conditions by which democracy can flourish” sounds unnatural; “by which” suggests method, not circumstances. Step 4: Test “for”: “conditions for which democracy can flourish” is awkward and incorrect; “conditions for” would normally be followed by a noun, not a clause starting with “which”. Step 5: Test “under”: “conditions under which democracy can flourish” is a standard expression, meaning the circumstances in which democracy can grow. Step 6: Test “at”: “conditions at which democracy can flourish” is ungrammatical in this context and does not fit the meaning. Step 7: Conclude that “under” is the only preposition that produces a natural and correct phrase.

Verification / Alternative check:
Read the entire sentence with “under”: “The conditions under which democracy can flourish are difficult to define; but one thing is clear, that democracy is always a slow growth.” This reads smoothly and matches typical usage in academic and political writing. Replacing “under” with any other option makes the sentence sound wrong or confusing, confirming that “under” is the correct choice.

Why Other Options Are Wrong:
“by” would suggest the means by which something happens, not the conditions in which it can exist. “for” does not work with the relative pronoun “which” in this structure and breaks the grammar. “at” is used with specific times or places, not abstract “conditions” followed by a relative clause.

Common Pitfalls:
A common error is to rely only on literal meaning and ignore set phrases. Learners sometimes choose “for” because they have seen “conditions for growth”, but they do not notice the relative clause “which democracy can flourish”. In this pattern, native speakers almost always say “conditions under which”. When in doubt, think of similar examples you know, such as “the circumstances under which”, or “the rules under which”.

Final Answer:
The correct preposition is under.