At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Law of syllogism: "If p, then q" is true, and "If q, then r" is true, then you can conclude "If p, then r" is true.
Here is an example: Use the law of syllogism with the two sentences: If it rains, then the road gets wet. If the road gets wet, then the car will skid. Conclusion: If it rains, the car will skid.
Now try doing this with your 3 questions.
Law of Detachment If p, then q. Given p is true. Conclude q is true.
In 7, you are given If p, then q. Then you are told q is true. This is not a case of the Law of Detachment.
8. is a case of the Law of Detachment. 9. is not.
I'll show you the first one. If it is raining, the temperature is greater than 32 F. If the temperature is greater than 32 F, then it is not freezing outside. From the two statements above, using the Law of Syllogism, you can conclude: If it is raining, then it is not freezing outside. Then using "It is raining." and the Law of Detachment, you can conclude: "It is not freezing outside."