Logical reasoning PrepTest 125 · Section 4 · Question 14

Incorrect. There's no need to define all technical terms in an argument, unless the definition of that term is called into question or there's a potential shift in the definition. Here, the second "use" of fractal uses a referent ("these criteria"), so there's no shift in meaning.

Incorrect. The Expert doesn't rely on the claims of the researchers. Instead, she relies on their antenna fitting a certain criterion. Her argument is flawed in the implication of her facts, not the facts themselves.

Incorrect. This answer describes an absence of evidence flaw. However, the Expert doesn't conclude that the Researchers' claim is false because they've failed to prove it's true. Instead, she relies on a supposed (and flawed) counterexample.

Correct. Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Errors in Reasoning

Stimulus Summary:
Researchers' claim - Antenna works equally well at all frequencies → Symmetrical AND Fractal structure
New antenna - Symmetrical and fractal structure; not Works equally well at all frequencies
Conclusion - The Researchers' claim is wrong

Answer Anticipation:
The Expert here reaches a conclusion about the Researchers' claim, so it's important to note whether that conclusion is that the opposing point is unsupported/invalid, or whether it's wrong/false. In stating that the claim is "incorrect," the Expert's conclusion falls into the latter category. As such, the argument needs to establish that the opposite conclusion is true, not just that there's a flaw in the logic.

That initial claim establishes two things that are necessary for an antenna to work equally well at all frequencies. Any statement that establishes requirements can be represented with conditional logic, which is represented in our summary.

The Expert is attempting to prove that this conditional relationship is wrong. In order to disprove a conditional, one must establish that the sufficient conditions are present without the necessary conditions—in other words, to show that the necessary conditions aren't actually necessary, because you can have the sufficient condition without them.

However, the Expert doesn't establish a situation where the sufficient condition is met but the necessary conditions aren't. Instead, she establishes a situation where the necessary condition is met but the sufficient condition isn't. Her "counterexample" is actually the illegal negation of a counterexample. The correct answer should highlight this Sufficient/Necessary flaw.

Answer Explanation:
This answer highlights the Sufficient/Necessary flaw (though using slightly different phrasing than we expected). The Researchers claim that an antenna with a specific characteristic has two necessary conditions. A counterexample would show an antenna with the characteristic but missing at least one of the necessary conditions. Instead, the counterexample presented by the Expert had the necessary conditions but was missing the sufficient—which only serves as a counterexample if she's confusing the necessary conditions for sufficient. This answer represents the flaw in her counterexample, so it's correct.

Key Takeaway:
Counterexamples are effective at disproving conditional statements, but they need to establish that the sufficient condition is present without the necessary condition.

Incorrect. This answer would be correct in an argument that neglects to consider the possibility of exactly 250 megahertz. However, the argument discusses the frequencies here to show that the antenna in question doesn't work equally well at all frequencies, and as such there's no need to consider all frequencies. In fact, the Expert could have established that with only two frequencies.