Unformatted text preview: E.g., on this last one, at line 11, we could have used 7 and 10 to get Q instead of 3 and 10 to get ⇠ P . This would also have given us a different contradiction (lines 3 and 11). Either way you do it is Fne.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. P ! ( N & M ) Q _⇠ N ⇠ ⇠ ⇠ SHOW: ⇠ ( P & ⇠ Q ) P & ⇠ Q ⇠ ⇠ ⇠ SHOW: 6 P ⇠ Q N & M ⇠ N N 6 Pr Pr ID Ass DD 4 &O 4 &O 1,6 ! O 2,7 _ O 8 &O 9,10 6 I There are, strictly speaking, two forms of indirect proof. The above are all examples of assuming that something is true in order to prove that it is false. We can also assume that something is false in order to prove that it is true. This form works almost exactly the same. Here are two examples. 1. 2. 3. 4. 5. 6. 7. 8. P _ Q Q ! P ⇠ ⇠ ⇠ SHOW: P ⇠ P ⇠ ⇠ ⇠ SHOW: 6 Q P 6 Pr Pr ID Ass DD 1,4 _ O 2,6 ! O 4,7 6 I 8...
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 Spring '08
 BOHN
 Logic

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