- Mon Oct 14, 2024 6:38 pm
#109906
Hi eunise,
First, the word "any" appears in both Answer A and Answer C. "Any" is a sufficient indicator word, similar to "if, when, all." A very helpful list of sufficient and necessary indicator words is found in "The Logical Reasoning Bible" under the chapter on conditional reasoning. If you haven't done so already, I'd recommend studying this list and actively be on the lookout for these words whenever you're doing LR problems.
Before looking at this argument, it may be helpful to look at a (hopefully) simpler example.
Imagine the following argument.
Premise: John lives in Texas.
Conclusion: Therefore, John lives in the United States.
What would we need to justify/prove this conclusion? We would need a conditional answer that has Texas in the sufficient condition and the United States in the necessary condition, such as:
If someone lives in Texas, then that person lives in the United States.
If we add this statement to the argument, then it proves the conclusion that John lives in the United States.
Another way of saying the same statement would be:
Anyone who lives in Texas lives in the United States.
("Anyone" is a sufficient indicator, just like "any.")
In each of those sentences, "lives in Texas" is the sufficient condition, and "lives in the United States" is the necessary condition. In other words, we want the premise "lives in Texas" to be the sufficient condition and the conclusion "lives in the United States" to be the necessary condition so that we can get from the premise to the conclusion. In other words, the premise will then prove the conclusion because the premise would be sufficient to guarantee the conclusion based on the conditional statement.
However, imagine that there was another answer that has the terms backwards, such as:
If someone lives in the United States, then that person lives in the Texas.
This answer would not prove the conclusion, because we're trying to show that living in Texas proves that one is living in US, not the other way around. This answer would be a Mistaken Reversal of what we want. The way that this answer is worded, living in Texas does not prove that someone lives in the United States.
In this argument, we want to go from "a place where you can buy well-maintained, used exercise machines at reasonable prices," which gyms and fitness centers are mentioned as being in the premise to "a good place to buy exercise machines," which gyms and fitness centers are mentioned as being in the conclusion.
The basic argument is:
Premise: Gyms and fitness centers are places where you can buy well-maintained, used exercise machines at reasonable prices.
Conclusion: Gyms and fitness centers are good places to buy exercise machines.
What we want is an answer that says,
If there's a place where you can buy well-maintained, used exercise machines at reasonable prices, then that is a good place to buy exercise machines.
Another way to say this is:
Any place where you can buy well-maintained, used exercise machines at reasonable prices is a good place to buy exercise machines. This is Answer C.
Answer A is backwards in the same way that the statement "If someone lives in the United States, then that person lives in the Texas." was backwards in the example above. In both, the conclusion appears as the sufficient and the premise as the necessary, but we need the premise to be sufficient and the conclusion to be the necessary so that we can go from the premise to the conclusion.
One final point, while this question is technically a strengthen question rather than a Justify question, the discussion above still would apply. When you have conditional answers, as we do here, to strengthen the argument you need the conditional statement to match the logic of the argument, going from the premise to the conclusion (and not backwards). Of course, an answer could always be in the form of the contrapositive, so be on the lookout for this as well.
offers some well-maintained machines at reasonable prices
