Self-paced
Interior decorator: All coffeehouses and restaurants are public places. ████ █████████████ ██████ ██████ ███████ ████████ ███ ██ █ ██████ █████ ██ █████████████ ██ ██ ███ ████ █████████ ███ ███ ███████████ ██████ ██████ ████ ████████ ██████████
The Given Rules
Rule 1: if a place is a coffeehouse, it is a public place; if it is a restaurant, it is a public place.
Rule 2: most well-designed public places feature artwork.
Rule 3: if a public place is uncomfortable, it is not well-designed.
Rule 4: if a public place is comfortable, it has a spacious interior.
Anticipation
Based on the contrapositive of Rule 3: if a public place is well-designed, then it is not uncomfortable. And "not uncomfortable" means "comfortable," since uncomfortable means not comfortable. Then Rule 4 kicks in, because comfortable public places have spacious interiors.
So well-designed leads to comfortable, which leads to a spacious interior. Coffeehouses and restaurants are public places (Rule 1), so this applies to them.
well-designed
→
comfortable
→
spacious interior
well-designed means not uncomfortable, which is comfortable (Rule 3), and all comfortable public places have spacious interiors (Rule 4)
25.
If all of the interior ███████████ ██████████ ███ █████ ████ █████ ███ ██ ███ █████████ ████ ██ █████
a
Any restaurant that ███ █ ████████ ████████ ██ ████████████
Could be false. We know all public places that are comfortable have spacious interiors. That doesn’t imply all public places with spacious interiors are comfortable. They might be uncomfortable places despite having spacious interiors.
b
Most public places ████ ███████ ███████ ███ ████ █████████
Could be false. We know most well-designed public places feature artwork. That doesn’t mean most public places featuring artwork are well-designed. Most A is B doesn’t imply Most B is A.
c
Most coffeehouses that ███ ████ ████████ ███████ ████████
Could be false. We know most well-designed public places feature artwork. Coffeehouses are just one kind of public place. The well-designed public places that feature artwork might just be other kinds of public places besides coffeehouses.
d
Any well-designed coffeehouse ██ ██████████ ███ █ ████████ █████████
Must be true. Coffeehouses and restaurants are public places (Rule 1), so the public-place rules apply to them. If one is well-designed, then by the contrapositive of Rule 3 it is not uncomfortable, which is to say comfortable. And Rule 4 says all comfortable public places have spacious interiors. So a well-designed coffeehouse or restaurant has a spacious interior.
Lots of people push back on treating "not uncomfortable" as "comfortable." The worry is that there might be a middle ground, a place that is neither comfortable nor uncomfortable, so that ruling out uncomfortable doesn't get you all the way to comfortable.
The reason it works here is in the word itself. "Uncomfortable" just means "not comfortable," since "un" is negation. So a place is either comfortable or uncomfortable, with nothing in between, and "not uncomfortable" is a double negative that lands back on "comfortable." This isn't a situation like "short" and "tall" where there's a middle ground. If "untall" were a word, then between "untall" and "tall" there would be no middle ground.
e
Any coffeehouse that ███ █ ████████ ████████ ██ █ █████████████ ██████ ██████
Could be false. We know well-designed public places have spacious interiors. That doesn’t imply all public places with spacious interiors are well-designed. There could be some public places with spacious interiors that are not well-designed.