Concept:The correct preposition required after the fixed idiom "lay siege" is "to".
Explanation:"Lay siege" is a set idiomatic expression that means to surround a town, building, or place with armed forces in order to capture it or force the people inside to surrender.
In standard English, this expression is always followed by the preposition "to" when stating the target or location of the siege.
The correct grammatical pattern is: "lay siege to" + the place.
For example, we correctly say "lay siege to the castle", but never "lay siege on the castle".
Therefore, the complete sentence should be: "The soldiers lay siege to the town to arrest the terrorists."
Options A, C, and D use the prepositions "on", "with", and "by", none of which form a valid idiom with "lay siege".
Answer:B. siege to