91Ó°ÊÓ

The National Association of Fire Fighters says that 45 percent of homes now have smoke detectors, whereas only 30 percent of homes had them 10 years ago. This makes early detection of house fires no more likely, however, because over half of the domestic smoke detectors are either without batteries or else inoperative for some other reason. In order for the conclusion above to be properly drawn, which one of the following assumptions would have to be made? (A) Fifteen percent of domestic smoke detectors were installed less than 10 years ago. (B) The number of fires per year in homes with smoke detectors has increased. (C) Not all of the smoke detectors in homes are battery operated. (D) The proportion of domestic smoke detectors that are inoperative has increased in the past ten years. (E) Unlike automatic water sprinklers, a properly functioning smoke detector cannot by itself increase fire safety in a home.

Step by step solution

01

Understanding the Conclusion

The conclusion is that the increase in homes with smoke detectors has not made early detection of house fires more likely, as more than half of these detectors are inoperative.

02

Identifying the Necessary Assumption

To arrive at this conclusion, the assumption needed is that the proportion of inoperative smoke detectors is higher now compared to ten years ago. This supports the notion that having more smoke detectors does not lead to better early fire detection.

03

Evaluating Answer Choices

Let's assess each option to see if it connects with the assumption needed: - (A) Doesn't address the operability issue. - (B) Doesn't relate to early detection capacity. - (C) Irrelevant to the inoperative nature. - (D) Directly addresses the increased proportion of inoperative detectors. - (E) Focuses on the functionality conditions of detectors, not the issue at hand.

04

Conclusion

The necessary assumption is best stated in option (D), which supports the idea that the increase in smoke detectors hasn't improved early detection due to a higher proportion of them being inoperative.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logical Assumptions

Logical assumptions play a crucial role in helping us connect different pieces of information to form a coherent argument. In the exercise, there's a clear headline assumption needed to justify the conclusion made about smoke detectors. The critical assumption here is that, despite more homes having smoke detectors, early detection of fires hasn't improved because many detectors are inoperative. This highlights a logical assumption that more smoke detectors do not equate to better safety unless they are functional.
Logical assumptions require us to think about the unseen or unspoken variables in a statement. In this case, it's not just about the number of smoke detectors, but their operational status. Here are some points to help you understand logical assumptions:

• Identify the gap between known facts and the conclusion.
• Consider factors that aren't directly mentioned but influence the conclusion.
• Remember that assumptions fill in the missing links in an argument.

Logical assumptions challenge us to consider what must be true for a conclusion to hold, even if it's not explicitly stated.

Argument Analysis

Argument analysis involves dissecting the argument to assess its validity and strength. In the exercise, we have a factual premise: more homes have smoke detectors now than a decade ago. The conclusion drawn is that this hasn't led to better early detection of fires. To analyze this argument, we must consider whether the conclusion logically follows from the given premises.
One method of argument analysis is identifying if all relevant facts are presented and if any assumptions are needed to connect them. In the given conclusion, the analysis involves checking if the condition of the smoke detectors (many being inoperative) adequately explains why early detection hasn't improved. Let's break it down:

• Does the premise support the conclusion? Only if the assumption about inoperative detectors holds true.
• Are any implicit claims stated or implied? Yes, that having more detectors itself isn’t enough for improved safety.
• Examine the context, especially the functionality mentioned, which is central to the argument's strength.

This thorough examination helps determine if the argument stands strong or if it requires additional support or assumptions.

Reasoning Skills

Reasoning skills help us critically evaluate arguments and form sound judgments. In the exercise, reasoning skills were applied to bridge the gap between an increase in smoke detectors and the unchanged likelihood of early fire detection. Such skills allow us to scrutinize each part of the argument and think of all possible factors involved.
To enhance reasoning skills, one must be able to differentiate between relevant and irrelevant information, spot flaws, and see hidden assumptions. Here’s how reasoning skills can be applied to this problem:

• Assess the premises critically: just having more of something (smoke detectors) doesn't automatically imply a qualitative benefit (improved early detection).
• Predict possible objections such as proving why so many detectors are inoperative.
• Develop alternative scenarios that might affect the conclusion, like changes in public awareness or improved fire safety measures.

By employing reasoning skills, one can better grasp the nuances in such arguments and be prepared to construct or deconstruct them logically and systematically.