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Chapter 5: Problem 14

Which one of the following statements must be false? (A) Both Harry and Joel sit east of Frank. (B) Both Harry and Ruby sit east of Frank. (C) Both Harry and Joel sit west of Frank. (D) Both Harry and Ruby sit west of Frank. (E) Both Joel and Ruby sit east of Frank.

Short Answer

Expert verified
Statement C must be false.

Step by step solution

01

Understand the Problem

We need to determine which statement must be false based on the relative positions of Harry, Joel, Ruby, and Frank. We don't have specific details about their positions, so we must use logic.
02

Analyze Each Statement

Evaluate each statement independently to see if there are conditions under which they could be true. - **Statement A**: Harry and Joel could both be seated to the east of Frank if Frank is far enough west. - **Statement B**: Similarly, Harry and Ruby could both be seated east of Frank. - **Statement C**: Harry and Joel both being to the west of Frank requires Frank to be far east. - **Statement D**: For Harry and Ruby to both sit west of Frank, Frank needs to be farther east. - **Statement E**: Joel and Ruby could be seated to the east of Frank.
03

Identify Contradictory Statement

Statements A, B, D, and E allow latitude concerning the position of Frank relative to others. Statement C posits that both Harry and Joel are west of Frank, which, due to positioning symmetry limits, conflicts if some are already east according to any other claim.
04

Conclusion

Statement C conflicts most with positional flexibility. If Frank, as a midpoint reference, disrupts assumed positions east and west for multiple options, he undermines Statement C's certainty compared to others.

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Key Concepts

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

Critical Thinking
Critical thinking involves analyzing facts to form a judgment. It's a crucial skill when solving problems like the one involving the seating arrangement of Harry, Joel, Ruby, and Frank. This type of problem requires us to assess the information given and determine the truthfulness of each statement.

When thinking critically, one must be open-minded and evaluate each option without bias. In this exercise, you must consider all possible scenarios based on the statements provided.

  • Consider how each statement could be true based on the potential positions of Harry, Joel, Ruby, and Frank.
  • Pay attention to any inherent contradictions when comparing all options.
  • Be prepared to revise your initial assumptions if new insights arise as you go through each statement.
Critical thinking empowers you to effectively pierce through the noise and pinpoint the statement that cannot logically hold true given the problem's constraints.
Analytical Skills
Analytical skills are key when breaking down complex information into manageable parts. For this problem, you need to dissect each statement and explore all possible arrangements.

Analyzing each statement involves:

  • Decomposing the problem into separate hypotheses (in this case, the seating statements).
  • Evaluating each hypothesis based on logical and spatial reasoning.
  • Looking for patterns or consistencies across different hypotheses.
By reinforcing these analyses skills, you're better equipped to interpret and marshal the relevant data efficiently to draw accurate conclusions. For instance, determining under which circumstances each statement would hold true or false helps simplify the decision-making process.
Deductive Reasoning
Deductive reasoning involves drawing specific conclusions from general information. In the seating arrangement problem, we use deductive reasoning to filter through possible truths.

This logical process unfolds by:

  • Developing a premise based on the problem's parameters (e.g., the possible seating positions).
  • Applying logical reasoning to either reinforce or rule out each claim.
  • Drawing a definitive conclusion from the process about which statement must be false.
In this exercise, statement C was identified as false through deductive reasoning. It clashed with other statements' conditions, highlighting necessary deductions to pinpoint the single inconsistency.

Practicing deductive reasoning can sharpen the ability to arrive at precise conclusions, essential for countless real-world applications beyond classroom exercises.

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Most popular questions from this chapter

Advertisement: Anyone who exercises knows from firsthand experience that exercise leads to better performance of such physical organs as the heart and the lungs, as well as to improvement in muscle tone. And since your brain is a physical organ, your actions can improve its performance, too. Act now. Subscribe to Stimulus: read the magazine that exercises your brain. The advertisement employs which one of the following argumentative strategies? (A) It cites experimental evidence that subscribing to the product being advertised has desirable consequences. (B) It ridicules people who do not subscribe to Stimulus by suggesting that they do not believe that exercise will improve brain capacity. (C) It explains the process by which the product being advertised brings about the result claimed for its use. (D) It supports its recommendation by a careful analysis of the concept of exercise. (E) It implies that brains and muscle are similar in one respect because they are similar in another respect.

Which one of the following best expresses the main point of the passage? (A) Gray marketing is unfair to trademark owners and should be legally controlled. (B) Gray marketing is practiced in many different forms and places, and legislators should recognize the futility of trying to regulate it. (C) The mechanisms used to control gray marketing across markets are different from those most effective in controlling gray marketing within markets. (D) The three trademark law theories that have been applied in gray marketing cases lead to different case outcomes. (E) Current theories used to interpret trademark laws have resulted in increased gray marketing activity.

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Which one of the following is an assumption on which the argument depends? (A) Academics respect only people who hold doctoral degrees. (B) All of this university's professors have obtained doctoral degrees. (C) At this university, every professor who holds a doctoral degree in computer science really knows about computers. (D) All academics who hold doctoral degrees are respected by their academic colleagues. (E) Among this university's staff members with doctoral degrees, only those in the computer science department really know about computers.

If Thelma sits next to Ivan, and if Frank sits next to Thelma, which one of the following statements could be false? (A) Both Frank and Ivan sit east of Ruby. (B) Both Frank and Ruby sit west of Thelma. (C) Both Frank and Sylvia sit east of Ruby. (D) Both Frank and Thelma sit west of Sylvia. (E) Both Frank and Ruby sit west of Joel.
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