Problem 57 - Thinking Mathematically

Question

Choose the correct statement. 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 airport would remain open. The City Council did not keep its promise during the first blizzard of the season. Therefore, during the first blizzard: a. No major roads connecting the city to the airport were open. b. At least one major road connecting the city to the airport was not open. c. At least one major road connecting the city to the airport was open. d. The airport was forced to close.

Step-by-Step Solution

Answer

The correct statement is (b). At least one major road connecting the city to the airport was not open, thus the City Council did not keep its promise.

Step 1: Understanding the Situation

The City Council promised all major roads to the airport would remain open in the event of snow. However, they didn't keep this promise during the first blizzard. From these facts, specific conclusions can be drawn.

Step 2: Analyzing Option (a)

Option (a) suggests that no major roads connecting the city to the airport remained open. This is a possible scenario, but the information in the text does not necessarily confirm this. Breaking a promise to keep all roads open could mean at least one road was closed, not necessarily all of them.

Step 3: Analyzing Option (b)

Option (b) suggests that at least one major road connecting the city to the airport was not open. This aligns with the council failing to keep its promise. As long as one road was closed, the council's promise is broken, which is what happened during the first blizzard.

Step 4: Analyzing Option (c)

Option (c) suggests that at least one major road connecting the city to the airport was open. This could be true and simultaneously, the council could still have broken its promise if not all roads were open.

Step 5: Analyzing Option (d)

Option (d) suggests that the airport had to close. The given information does not provide any insight into the airport’s operations during the blizzard, hence, it cannot be concluded that the airport was forced to close.

Key Concepts

Deductive Reasoning

Deductive reasoning is a logical process where conclusions are drawn from general statements or premises about specific instances. This means if the premises are true, the conclusion must also be true. In the exercise, the city council's promise serves as the premise: all major roads to the airport would remain open during snow. The first blizzard scenario provided an instance where this promise was unfulfilled. Using deductive reasoning, we assess each statement to determine the truth.

• For example, if the promise is broken, at least one road must not be open.
• This leads us to eliminate answer choices that don't align logically with the initial promise being unmet.

This type of reasoning helps eliminate illogical or unsupported conclusions by systematically analyzing given premises.

Problem-Solving

Problem-solving involves identifying the issue at hand and using a series of steps to arrive at a solution. In this exercise, the problem is understanding which statement accurately reflects the city council's broken promise.

• First, identify the main information: the promise to keep roads open.
• Next, examine each option to check if it aligns with the premise or deviates from it.

Using logical analysis, you assess each statement, filtering out those that don't satisfy the conditions. This structured approach helps you determine the most reasonable and supported answer.

Critical Thinking

Critical thinking is the ability to analyze facts to form a judgment. This skill is crucial when assessing the validity of arguments or statements. In the exercise, you need to scrutinize the given situation and options closely, considering which answer truly reflects the failure of the city council's promise.

• Think about what it means for a promise to be broken - not all roads were open as promised.
• Consider the implications of each option, and if they logically follow from the situation.

By applying critical thinking, you can objectively analyze and evaluate the arguments, reaching the conclusion that matches the logical analysis of the premises.