Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements. If you do not get enough sleep, then you will be tired. If you are tired, then you cannot pay attention in school. You only got three hours of sleep on Tuesday night. You only got three hours of sleep on Tuesday night. You cannot pay attention in school on Wednesday. You did not get enough sleep on Tuesday night. You are tired on Wednesday.
To use the Law of Detachment and the Law of Syllogism to draw a conclusion, we need to identify the given statements and determine the logical deductions we can make from them.
Given statements:
1. If you do not get enough sleep, then you will be tired.
2. If you are tired, then you cannot pay attention in school.
3. You only got three hours of sleep on Tuesday night.
Applying the Law of Detachment, we can conclude:
- If you do not get enough sleep, then you will be tired. Since you only got three hours of sleep on Tuesday night, it implies that you did not get enough sleep on Tuesday night.
Now, applying the Law of Syllogism, we can make another deduction:
- If you did not get enough sleep on Tuesday night, then you will be tired. Since you did not get enough sleep on Tuesday night, it implies that you will be tired.
Hope this helps!
By applying the Law of Detachment and the Law of Syllogism to the given statements, we can draw the following conclusions:
1. If you do not get enough sleep, then you will be tired. (Given)
2. If you are tired, then you cannot pay attention in school. (Given)
3. You only got three hours of sleep on Tuesday night. (Given)
Using the Law of Detachment, we can conclude:
4. You did not get enough sleep on Tuesday night. (Statement 3)
Using the Law of Syllogism, we can conclude:
5. You are tired on Wednesday. (Statement 1 and 4)
6. If you are tired, then you cannot pay attention in school. (Given)
Therefore, the final conclusion is:
7. You cannot pay attention in school on Wednesday. (Statement 6 and 5)
To draw a conclusion from the given statements using the Law of Detachment and the Law of Syllogism, let's break it down step by step:
1. Statement 1: If you do not get enough sleep, then you will be tired.
2. Statement 2: If you are tired, then you cannot pay attention in school.
3. Statement 3: You only got three hours of sleep on Tuesday night.
Using the Law of Detachment, we can conclude that:
- If you do not get enough sleep (based on Statement 3), then you will be tired (based on Statement 1).
Now, let's move on to the next set of statements:
4. Statement 4: You cannot pay attention in school on Wednesday.
5. Statement 5: You did not get enough sleep on Tuesday night (concluded from Statement 3).
Using the Law of Syllogism, we can combine the conclusions from the previous steps:
- You did not get enough sleep on Tuesday night (Statement 5) and if you do not get enough sleep, then you will be tired (conclusion from Law of Detachment). Therefore, you are tired on Wednesday.
Hence, the conclusion drawn using the Law of Detachment and the Law of Syllogism is that you are tired on Wednesday.