Please refrain ... smoking in the restaurant Nobody knows who is responsible ... the arson

1. Please refrain from smoking in the restaurant: "from" is the correct preposition to use here. The phrase "refrain from" means to stop oneself from doing something. In this context, it is a polite request for customers to avoid smoking within the restaurant premises. The use of "from" indicates that smoking is the action being stopped.

2. Nobody knows who is responsible for the arson: "for" is the appropriate preposition in this case. The phrase "responsible for" indicates accountability or obligation in relation to a specific action or event. In this sentence, it indicates that someone is accountable for the act of arson, which refers to deliberately setting fire to property. The use of "for" connects the subject ("who") to the action ("the arson") being discussed.