Why is it that “some” and “most” are contrapositives? I know “some” is ambiguous possibly meaning half, more than half, or fewer than half but I don’t understand why the “most” is the contrapositive as opposed to fewer than or exactly half.
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I have to say this question at first glance appeared difficult. However, applying the repetitiveness of these drills after the office hours lectures is becoming second nature, helping me reason logically. I knew the contrapositives of some right away, and most from the lecture notes argument began to make sense. I have to say, though, I was cringing when I selected the answer. However, when I saw that I had selected the correct answer, I was overjoyed. We have to practice and listen to the office hour lectures. One more thing I had to come to terms with is the abstract argument setups. They were confusing initially because I'm use to viewing the argument worded. Thanks guys.
Jay-EtterJanuary 28, 2022
Hi @Emdaf and @Lamont,
I wanted to point out two things on this one. First, remember that "contrapositive" refers specifically to conditional statements (such as A->B when we reverse and negate to get Not B -> Not A).
Secondly, let's look at this question. P1: Not A -> Not B // B -> A P2: B-most-X C?
So if all B's are A's, and Most B's are Xs, we know that there is at least some overlap between A and X. However, we don't know that most As are Xs, because we don't know that most As are Bs. If we put this one into words while keeping the exact same premises:
P1: If dog -> animal P2: Most dogs have fur C?
We wouldn't conclude that most animals have fur, because dogs are only a small percentage of all animals. However, at least some animals must have fur, because most dogs have fur and all dogs are animals!
Our conclusion would be some animals have fur.
Samantha74April 5, 2023
Can you recommend a office hour for these drills?
Emil-KunkinApril 7, 2023
Hi, I would recommend office hours that focus on quantifiers and sufficient and necessary, as well as strengthen with sufficient premise questions.
Samantha74April 10, 2023
In the Argument Completion Drills A- NOT B C-B NOT D - A C: NOT D -NOT C
I got C-D my question is how do you where to start the chain I wrote out C-B-NOT A-D and got C-D
