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Unformatted text preview: Some Full Truth-Tables from Lecture
Philosophy 12A September 23, 2008 1 Truth-Tables for Individual Statements (Logical Truth, etc.) Here are solutions to some of the problems from lecture about logical truth, logical falsity, and contingency of individual LSL sentences. In the truth-tables, the blue columns are the main connectives, and the others are quasi-columns. I have numbered the columns in the order in which I have done the computations (actually, my computer program made these!). 3. `(S R) & (S & R)' is logically false (self-contradictory): R S S R & S& R 2 4 3 1 4. `((E F ) F ) E' is contingent: EF E F F E 1 2 3 12. `[(H N) & (T N)] [(H T ) N]' is logically true (tautologous): HNT H N & T N H T N 3 5 2 6 1 4 15. `[(F E) & (G H)] [(G & E) (F & H)]' is contingent: EFGH F E & G H G&E F&H 4 6 3 7 2 5 1 2 Truth-Tables for Pairs of Statements (Equivalence, etc.)
3. `H G' and `(G & H) (G & H)' are contradictory: G HH G H G&H G G& H 2 1 3 5 2 4 1 4. `N & (A E)' and `A & (E N)' are inconsistent (but not contradictory): A E NN& A A E N A& E E N 3 2 1 2 4 3 1 6. `R & (Q S)' and `(S R) & (Q R)' are consistent (but not equivalent): Q R SR& Q R S S R & Q R Q S 2 1 2 3 1 8. `Q (K F )' and `(K & Q) (F & Q)' are contradictory: F K QQ F Q K KF K & Q F&Q 3 2 1 2 3 1 ...
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- Spring '08