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Reflect: To make your argument deductively valid, you will need to make sure that there is no possible way that your premises could be true and your conclusion false. Your premises must lead logically to the truth of your conclusion. Make sure that your argument is sound, that is in addition to being valid, make sure that the premises are true as far as you can tell. If your argument is invalid or if it has a false premise, revise it until you get an argument that you can stand behind. Write: Identify the components and structure of your argument by presenting your deductively valid argument in standard form, and explain how your conclusion follows from your premises. Guided Response: Read the arguments presented by your classmates, and analyze the reasoning that they have presented. In particular, if you believe that their argument is invalid, explain a way in which it would be possible for the premises to be true and the conclusion false. If you believe that their argument has a false premise, explain why a reasonable person might take it to be false. Finally, see if you can help them to improve their argument. How can they alter their premises so that all of them are true? What might they change in order to make their argument valid?Write: Choose three of the logical forms from the list below. (You may use the same form as someone else, but to not use any of the same examples.) Use standard form to present an instance of each of the three logical forms. For each form, provide a brief discussion of whether or not the form is logically valid and why. If it is valid, try to explain why the conclusion must be true provided that the premises are. If it is not valid, try to explain how it would be possible for the premises to be true and the conclusion false.

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Here are your options:

Categorical Forms (the variables represent categories):

1. All As are Bs. No Cs are Bs. Therefore, no Cs are As.

2. Some As are not Bs. No Bs are C. Therefore, some Cs are not As.

3. Some As are Bs. Some Bs are Cs. Therefore, some As are Cs.

4. Only As are Bs. Some Bs are Cs. So some Cs are As.

5. All As are Bs. Some Bs are not Cs. Therefore, Some Cs are not As.

6. No As are Cs. Some Bs are Cs. So some As are not Bs.

7. No As are Cs. Some Bs are Cs. So some Bs are not As.

Sorites (Sorites = “heaps”: these have more than 2 premises):

8. All As are Bs. All Bs are Cs. Some Cs are Ds. Therefore, some As are Ds.

9. All As are Bs. All Bs are Cs. Some As are Ds. Therefore, some Cs are Ds.

10. All As are Cs. Some Cs are Ds. All Ds are Bs. Therefore, some As are Bs.

11. Only As are Bs. No Ds are Bs. Some Ds are Cs. Therefore, some As are Cs.

12. Only As are Bs. Some Ds are Bs. All As are Cs. Therefore some Ds are Cs.

Propositional Forms (the variables represent simple sentences):

13. If P then Q. If Q then R. Therefore, if P then R. (Can you name this form???)

14. If P then Q. Q. Therefore, P. (Can you name this form???)

15. If P then Q. P. Therefore Q. (Can you name this form???)

16. P or Q. Not P. Therefore, not Q (Can you name this form???)

17. If P then Q. Not Q. Therefore, not P. (Can you name this form???)

18. If P then Q. Not P. Therefore, not Q. (Can you name this form???)

19. P only if Q. Q. Therefore P.

20. P and Q. If P then R. Therefore, R.

21. P or Q. If P then R. Therefore, R.

22. P or Q. If P then S. If Q then S. Therefore S.

23. If P then Q and R. P and Q. Therefore, R.

24. If P or Q then R and S. P. Therefore S.

25. P and if Q then R. Not R. Therefore, P and not Q.

26. Neither P nor Q. R only if Q. Therefore, not R.

27. Neither P nor Q. If Q then R. Therefore, not R.

28. P if and only if Q. Not P and not S. Therefore, not Q.

29. P if and only if both Q and R. R but not Q. Therefore, not P.

30. If P then Q and R. Q and R. Therefore, P.

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