lecture17

lecture17 - UsesforConditionalProof We left off talking...

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    Uses for Conditional Proof We left off talking about how to use CP to derive biconditionals and disjunctions. To derive a biconditional p ↔ q, use conditional proof to derive p → q and q→p. Then conjoin the conditionals and use ME: p ↔ q :: (p → q) ● (q → p).
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    Using Conditional Proof To derive a disjunction, derive the conditional that is equivalent by ME, then use ME: p → q :: ~p v q An example: J → (K → L), J →(M →L), ~L .˙. ~J v ~(K v M)
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    Using Conditional Proof This derivation illustrates another case where CP can be useful: 1)  ~X v (O ● W) 2) (X O) (W X) .˙. W X 3) W Assume 4) X Assume 5) ~~X 4, DN 6) O ● W 1,5, DS 7) O 6, Simp 8) X O 4-7, CP 9) W X 2, 8, MP 10) X 3, 9, MP 11) W X 3-10, CP My initial assumption of W was not very helpful, so I used CP to  derive the antecedent of (2) and proceeded from there.
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  Collapsing Steps These proofs can get a little long. We can  shorten them by applying more than one rule  to a line. This is called  collapsing steps . This isn’t mandatory. If you feel more  comfortable writing out each step, I  encourage you to do so. This method is 
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This note was uploaded on 03/14/2010 for the course PHIL 3 taught by Professor Way during the Fall '08 term at UCSB.

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lecture17 - UsesforConditionalProof We left off talking...

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