Intro to Logic notes7

Intro to Logic notes7 - 7 Wednesday, July 18, 2007 10:12 AM...

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Unformatted text preview: 7 Wednesday, July 18, 2007 10:12 AM Barney is either fierce or friendly. If Barney is friendly then he is smiling. Barney is not smiling so he is fierce. Barney is either fierce or friendly. If Barney is friendly then he is smiling. Barney is not smiling. /Barney is fierce. Dictionary: F=barney is fierce R=barney is friendly S=barney is smiling (F v R); RS; ~S/F (((F v R)&(RS))&~S)F F T T T T F F F F R T T F F T T F F S T F T F T F T F F v R T T T T T T F F RS T F T T T F T T ~S F T F T F T F T T T T T T T T T F T T T T F F F F Formal Derivations 1) 2) 3) 4) 5) 1) 2) 3) 4) 5) P Pr PQ Pr QR Pr Q 1,2,MP R 3,4,MP ~R Pr PQ Pr QR Pr ~Q 1,3,MT ~P 2,4,MT 1) ~P Pr Intro to Logic Page 1 2) 3) 4) 5) ~P~R Pr QR Pr ~R 1,2,MP ~Q 3,4,MT MP and MT are known as inference rules. We can also use MTP. A v B; ~A/B A v B; ~B/A Simple derivation Is a list of formulas which has the last line as the conclusion and all previous lines are inference rules or premises. 1) 2) 3) 4) 5) 6) P(Q v R) Pr P~R Pr P Pr Q v R 1,3,MP ~R 2,3,MP Q 4,5,MTP2 1) 2) 3) 4) 5) 6) 7) 8) 9) ~S Pr RS Pr R v ~T Pr ~P v T Pr ~P~Q Pr ~R 1,2,MT ~T 2,6,MTP1 ~P 4,7,MTP2 ~Q 5,8,MP Intro to Logic Page 2 ...
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