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Tuesday, July 17, 2007 10:02 AM Translating statements into sentential logic. Even if P even if Q can be read as P if Q = QP Only if P only if Q can be read as If P, then Q Example: My tree will grow only if it receives adequate light. T L If T, then L Dictionary T = My tree grows L= My tree receives adequate light Unless Suppose I promise you will not graduate (G) unless you pass logic (P). Only a lie if you graduate and don't pass logic. G unless P ~PG If and Only if P if Q QP AND P only if Q PQ Necessary/Must For you to graduate, it is necessary for you to pass logic. G L False when you graduate and don't pass. GL Sufficient It is sufficient that you ace every exam to pass logic. A L A=T L=F AL Intro to Logic Page 1 Necessary AND sufficient Not Necessary but sufficient Not necessary or sufficient 1 place ~_____ 2 place &, V, , 3 place Otherwise BA & & AB ~(AB) AB ~(AB) Necessary AND Not Sufficient BA ~(BA) & ~(BA) & If it is sunny I will play tennis. Otherwise I will play racquetball. (ST)&(~SR) Examples: If neither Jay nor Kay is working then we will go on vacation J=Jay is working K=Kay is working W=we go on Vacation ~(J v K)W J T T T T F F F F K T T F F T T F F W T F T F T F T F J v K T T T T T T F F ~(J v K) F F F F F F T T T T T T T T T F W T F T F T F T F You will pass unless you goof off, provided you are intelligent P=Pass G=goof off I=you are intelligent I(~GP) P T T T T F F F G T T F F T T F I T F T F T F T GP T T T T F F T ~(GP) I~(GP) F F F F T T F F T F T T T F Intro to Logic Page 2 F F F T F T If Sam didn't go to the shops, then we have nothing to eat or drink. He didn't go to the shops. SO we have nothing to eat or drink. Modus Ponens S=Sam went to the shops E= we have something to eat D= we have something to drink ~S~(E v D) ~S / ~(E v D) ((~S~(E v D))&~S)(~(E v D)) S T T T T F F F F E T T F F T T F F D T F T F T F T F ~S F F F F T T T T T T T T F F F T ~(E v D) & F F F T F F F T F F F F F F F T ~S F F F F T T T T T T T T T T T T ~(E v D) F F F T F F F T Tautology so the argument is valid. Therefore the premises logically imply the conclusion. Barney is either fierce or friendly. If barney is friendly then he is smiling. Barney is not smiling so he is fierce. Intro to Logic Page 3 ...
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 Spring '08
 Morgan
 Logic, Necessary and sufficient condition, Barney, If and only if, Logic Page, adequate light

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