Question

the city council of a large northern metropolis promised its citizens that in the event of snow, all major roads connecting the city to its subway stations would remain open. the city council did not keep its promise during the first blizzard of the season. write a statement that represents the situation.

choose the correct answer below

a. the subway stations were forced to close.
b. no major roads connecting the city to its subway stations were open.
c. at least one major road connecting the city to its subway stations was not open.
d. at least one major road connecting the city to its subway stations was open.

Explanation:

The City Council promised that all major roads connecting the city to subway stations would remain open during snow. Not keeping the promise means the negation of "all roads are open". The negation of "all \( x \) have property \( P \)" is "at least one \( x \) does not have property \( P \)". So, the situation is that at least one major road connecting the city to its subway stations was not open.

• Option A: The problem is about roads, not subway stations closing. Eliminate.
• Option B: "No major roads were open" is the negation of "at least one road was open", not the negation of "all roads were open". Eliminate.
• Option C: Matches the negation of the original promise (all open → at least one not open). Correct.
• Option D: This would mean the Council kept part of its promise, but the problem states they did not keep the promise. Eliminate.

Answer:

C. At least one major road connecting the city to its subway stations was not open