Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements. If you have an income, then you must pay taxes. If you have a job, then you have an income. You work as a cashier in a convenience store. You have a job. You work as a cashier. You must pay taxes. You have an income.

Question

Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements. If you have an income, then you must pay taxes. If you have a job, then you have an income. You work as a cashier in a convenience store. You have a job. You work as a cashier. You must pay taxes. You have an income.

Answer 1

Based on the given true statements, we can use the Law of Detachment and Law of Syllogism to draw the following conclusion:

1. If you have an income, then you must pay taxes. (Premise)
2. If you have a job, then you have an income. (Premise)
3. You work as a cashier in a convenience store. (Premise)
4. You have a job. (Premise)

Using the Law of Syllogism, we can combine statements 2 and 4 to form a new statement:

5. If you have a job, then you have an income.

Now, by applying the Law of Detachment, we can use statement 5 and statement 3 to draw a conclusion:

6. You have an income.

Therefore, based on the given information, we can conclude that you have an income.

Answer 2

To draw a conclusion using the Law of Detachment and the Law of Syllogism, let's analyze the given statements:

1. "If you have an income, then you must pay taxes." (Statement 1)
2. "If you have a job, then you have an income." (Statement 2)
3. "You work as a cashier in a convenience store." (Statement 3)
4. "You have a job." (Statement 4)

Now, using the Law of Syllogism, we can combine statements 2 and 4:

5. Since statement 4 says "You have a job" and the Law of Syllogism allows us to combine this with statement 2, we can infer "You have an income."

Now, using the Law of Detachment, we can use statement 1 and the conclusion we just drew:

6. Using statement 1 ("If you have an income, then you must pay taxes") and the conclusion we just drew ("You have an income"), we can infer "You must pay taxes."

Therefore, if you work as a cashier, based on the given statements and using the Law of Detachment and the Law of Syllogism, we can conclude that you must pay taxes.

Answer 3

To draw a conclusion using the Law of Detachment and the Law of Syllogism, we need to analyze the statements provided.

First, let's list the given statements:
1. If you have an income, then you must pay taxes. (Statement A)
2. If you have a job, then you have an income. (Statement B)
3. You work as a cashier in a convenience store. (Statement C)
4. You have a job. (Statement D)

Using the Law of Syllogism, we can combine statements B and D to derive a new statement:
5. If you have a job, then you have an income. (Statement B)
6. You have a job. (Statement D)
7. Therefore, you have an income.

Now, using the Law of Detachment, we can combine statement A with the conclusion from the previous step:
8. If you have an income, then you must pay taxes. (Statement A)
9. You have an income. (Conclusion - Step 7)
10. Therefore, you must pay taxes.

Therefore, the conclusion that we can draw using the Law of Detachment and the Law of Syllogism is: You must pay taxes.