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.