Rules of Replacement 1

# Rules of Replacement 1 - now simplify Which part should we...

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Natural Deduction Natural Deduction 7.3 © 2006 Kevin J. Browne

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Rules of Replacement I DeMorgan’s Rule Commutativity Associativity Distribution
DeMorgan’s Rule ~(p . q)  ::  ~p v ~q  ~(p . q)  ::  ~p v ~q  ~(p v q) ::  ~p . ~q  ~(p v q) ::  ~p . ~q

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Commutativity  Commutativity  p p v v q q p p . . q q
Associativity  Associativity  p p v v q q v v r r p p . . q q . . r r ( ( ( ( ) ) ) )

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Distribution  Distribution  p p v v q q . . r r ( ( ) ) ) ) ( ( ) ) p p . . q q v v r r ( ( ) ) . . ) ) ( ( ) )
An Example An Example 1. J v (K . L) 2. ~K                    /J Here we seem unable to use any  of the rules of inference  immediately. Let’s try a rule of replacement…                distribution?

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An Example An Example 1. J v (K . L) 2. ~K                    /J 3. (J v K) . (J v L)   1 dist. The advantage here is we can

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Unformatted text preview: now simplify! Which part should we simplify? We have a ~K in line two which is a clue! An Example An Example 1. J v (K . L) 2. ~K /J 3. (J v K) . (J v L) 1 dist. 4. J v K 3 simp. Now how can we get J out of line 4? Remember you can’t simplify a disjunction! But speaking of disjunctions there’s a DS! An Example An Example 1. J v (K . L) 2. ~K /J 3. (J v K) . (J v L) 1 dist. 4. J v K 3 simp. 5. J 2,4 DS And the code is solved!...
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Rules of Replacement 1 - now simplify Which part should we...

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