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It seems like you've got the basic idea, but there are some key concepts missing.
1. If A then if B, then C - Your answer is equivalent from a true/false sense, but the most accurate interpretation is A => (B => C)
7. Either A or if B then C - Note that A is not part of the if-then.
A U (B => C)
8. If not A then either not B or not C - You have to be careful when NOT interacts with AND or OR. If we know that either B OR C is NOT true, that is the same as saying they're NOT both true. So, (~B U ~C) is equivalent to ~(B * C).
~A => (~B U ~C)
Which is equivalent to ~A => ~(B * C)
9. If not A then both not B and not C - This is similar to the last one. If we know that both B AND C are NOT true, that is the same as saying it's NOT true that either B OR C is true. Thus, (~B * ~C) is equivalent to ~(B U C).
~A => (~B * ~C)
Which is the same as ~A => ~(B U C)
10. Not the case that if A then B and C - The NOT here is "outside" of the if-then.
~[A => (B * C)]
11. If not A then not B, and C - This one is worded rather poorly, in my opinion. I would have just said, "If Argentina does not mobilize, then..."
(~A => ~B) * C
13. B only if A - The logical convention diverges a little from the typical English meaning here. What this means is that B can be true only if A is true. In the case of A being true, B might be true or it might not. All we know for sure is that if A is NOT true, then B also is NOT true.
~A => ~B
14. C only if A and B - Same deal with the only if.
~(A * => ~C
15. B only if either A or C - Same thing.
~(A U C) => ~B
17. B unless C - Unless is a little similar to only if. B is true unless C is true, so if C is NOT true then B is true. But if C is true, we don't know whether B is true or not. Another way to think about it is that "unless" = "if not"; B if not C.
~C => B
18. If A then B unless C - Same as before.
A => (~C =>
19. Not B unless A - It works the same regardless of the NOT B.
~A => ~B
20. Unless C, B - Just a rewording of 17.
~C => B
21. A is a sufficient condition for B - You had this one right, but I just want to point out that the statement is equivalent to "A implies B".
22. A is a necessary condition for C - C can't be true if A is not true, so this is really the same as saying "C only if A".
~A => ~C
25. If neither C nor D, then not B unless A - This one is a little complicated, but it doesn't add anything new.
This is strangely similar to computer programming. Ask a computer programmer that has a philosophy minor perhaps?
That's not a bad idea, but I'd look first for a math major (with or without the philosophy minor). Math students use this stuff all the time in every last upper-level course.
This is strangely similar to computer programming. Ask a computer programmer that has a philosophy minor perhaps?
That's not a bad idea, but I'd look first for a math major (with or without the philosophy minor). Math students use this stuff all the time in every last upper-level course.
Posts
1. If A then if B, then C - Your answer is equivalent from a true/false sense, but the most accurate interpretation is A => (B => C)
7. Either A or if B then C - Note that A is not part of the if-then.
8. If not A then either not B or not C - You have to be careful when NOT interacts with AND or OR. If we know that either B OR C is NOT true, that is the same as saying they're NOT both true. So, (~B U ~C) is equivalent to ~(B * C).
Which is equivalent to ~A => ~(B * C)
9. If not A then both not B and not C - This is similar to the last one. If we know that both B AND C are NOT true, that is the same as saying it's NOT true that either B OR C is true. Thus, (~B * ~C) is equivalent to ~(B U C).
Which is the same as ~A => ~(B U C)
10. Not the case that if A then B and C - The NOT here is "outside" of the if-then.
11. If not A then not B, and C - This one is worded rather poorly, in my opinion. I would have just said, "If Argentina does not mobilize, then..."
13. B only if A - The logical convention diverges a little from the typical English meaning here. What this means is that B can be true only if A is true. In the case of A being true, B might be true or it might not. All we know for sure is that if A is NOT true, then B also is NOT true.
14. C only if A and B - Same deal with the only if.
15. B only if either A or C - Same thing.
17. B unless C - Unless is a little similar to only if. B is true unless C is true, so if C is NOT true then B is true. But if C is true, we don't know whether B is true or not. Another way to think about it is that "unless" = "if not"; B if not C.
18. If A then B unless C - Same as before.
19. Not B unless A - It works the same regardless of the NOT B.
20. Unless C, B - Just a rewording of 17.
21. A is a sufficient condition for B - You had this one right, but I just want to point out that the statement is equivalent to "A implies B".
22. A is a necessary condition for C - C can't be true if A is not true, so this is really the same as saying "C only if A".
25. If neither C nor D, then not B unless A - This one is a little complicated, but it doesn't add anything new.
The others are correct.
That's not a bad idea, but I'd look first for a math major (with or without the philosophy minor). Math students use this stuff all the time in every last upper-level course.
but how can I be sure you're not a knave?