#1

Here's my argument:

Alice went to Lincoln High and earned a college scholarship.
Ben went to Lincoln High and earned a college scholarhip.
Carol went to Lincoln High and earned a college scholarship.
Dan went to Lincoln High and earned a college scholarship.
Ellen goes to Lincoln High.
Therefore, Ellen will win a scholarship to college.

Now I am to determine wheather the addition of various premises weakens or strengthens the argument in terms of positive or negative analogy, relevance, and/or the number of observed cases. These are the premises I'm having difficulty with

1.) Alice, Ben, and Ellen took advanced courses in high school, whereas Carol and Dan did not take advanced courses.
(I would say that the argument is strengthened by increasing the negative analogy among the observed cases, but I'm not sure since it states that Ellen is like some of the other students in one regard way but unlike other students in that regard.)

2.) Alice, Ben, Carol, Dan got between 600 and 650 on their college boards, whereas Ellen got between 700 and 750 on her college boards.
(I would think that the addition of this premise would weaken the argument because it would be increasing the negative analogy between the observed and unobserved cases, but given an additional part to the exercise, I have reason to believe that it strengthens the argument.)

Thanks in advance for any help you can give me.

Although I am not trained in formal logic, it would seem that whatever traits — which are linked to getting scholarships — Ellen has that equal or exceed those of the others would lead to predicting that she would get the scholarship. In other words, they would strengthen the arguments.

I hope this helps. Thanks for asking.

To evaluate whether the addition of premises strengthens or weakens the argument, let's analyze each premise individually:

1) Alice, Ben, and Ellen took advanced courses in high school, whereas Carol and Dan did not take advanced courses.
This premise introduces a difference among the observed cases, indicating that Alice, Ben, and Ellen took advanced courses while Carol and Dan did not. This creates a negative analogy, suggesting that Ellen is more similar to Alice and Ben than to Carol and Dan in this regard.

In terms of the argument's strength, this addition may actually weaken it. While it strengthens the similarity between Ellen and Alice/Ben, it weakens the overall analogy because it highlights Ellen's difference from Carol and Dan. Therefore, it introduces some uncertainty about whether Ellen will also earn a college scholarship like Alice and Ben.

2) Alice, Ben, Carol, and Dan got between 600 and 650 on their college boards, whereas Ellen got between 700 and 750 on her college boards.
This premise introduces a difference in the observed cases, showing that Ellen's test scores are higher compared to that of Alice, Ben, Carol, and Dan. This creates a negative analogy, suggesting that Ellen may not be as similar to the others in terms of test scores.

Contrary to initial expectations, the addition of this premise actually strengthens the argument. Higher test scores generally correlate with scholarship opportunities, so Ellen's higher scores imply that she might have an even better chance of winning a scholarship than Alice, Ben, Carol, and Dan. This premise provides additional evidence that supports the conclusion that Ellen will win a college scholarship.

In summary, the first premise weakens the argument by highlighting a difference between Ellen and Carol/Dan, while the second premise strengthens the argument by indicating that Ellen's test scores are higher than those of Alice, Ben, Carol, and Dan.