Notes1 - Some Full Truth-Tables from Lecture Philosophy 12A...

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Unformatted text preview: Some Full Truth-Tables from Lecture Philosophy 12A February 16, 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 31 4. ‘((E → F ) → F ) → E ’ is contingent : EF EF F E 1 2 3 12. ‘[(H → N) & (T → N)] → [(H ∨ T ) → N]’ is logically true (tautologous ): HNT HN&TN HT N 3 5 2 6 1 4 15. ‘[(F ∨ E) & (G ∨ H)] ↔ [(G & E) ∨ (F & H)]’ is contingent : EFGH FE&GH G&E F&H 4 6 3 7 2 5 1 
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