complete these worksheets
Logic Worksheet: Propositional Logic Name:__________________________ Part I: Propositional Translations. Translate the following sentences into propositional language. 1. If you’re tall and boring, then you’re scholarly. 2. You’re dull and charitable, or else frightened. 3. If not R then P. 4. You’re smart, and remarkable or dishonest. 5. Not either not C or F. 6. You aren’t both not filthy and hideous. 7. You’re both clean and either fortunate or loveable. 8. You’re both not gloomy and miserable. 9. You’re either both short and humorous or else disgusting. 10. If not R then not P. 11. If you’re smart, then you’re dangerous or terrified. 12. Not if not C then T. 13. You’re either not wild or else scholarly. 14. Not both G and P. 15. Not either R or C. 16. If R then C, and F. 17. Not if W then C. 18. Not both F and C. 19. You’re either not cruel or not forgetful. 20. Not either not M or F. Part II: Truth Tables – Determine the truth-value of the complex expression given the atomic truth-values. 1. If A=1 and B=0, then “(AB)” = 2. If A=1 and B=1, then “(A v B)” = 3. If A=1, then “(A A)” = 4. If A=1 and B=0, then “(A B)” = 5. If A=1 and B=1, then “(A v B)” = 6. If A=0 and B=0, then “(A B)” = 7. If A=1 and B=0, then “(A v B)” = 8. If A=1 and B=0, then “(A B)” = 9. If A=1, then “(A v A)” = 10. If A=0 and B=1, then “(AB)” = 11. If A=0, B=0, and C=1, then “(~(AB) C)” = 12. If A=0, B=0, and C=1, then “~(A (~B ~C))” = 13. If A=1, B=0, and C=1, then “(A (B ~C))” = 14. If A=0, B=1, and C=0, then “~((A B) C)” = 15. If A=1, B=1, and C=1, then “~(A (~B C))” = 16. If A=1, B=1, and C=1, then “~(A v (~B ~C))” = 17. If A=0 and B=1, then “((~A B) A)” = 18. If A=1, B=0, and C=0, then “((A B) C)” = 19. If A=0, B=1, and C=0, then “((A ~B) C)” = 20. If A=0, B=1, and C=0, then “(A (B v ~C))” = 21. If A=0, B=?, and C=0, then “~(~A v (~B C))” = 22. If A=0, B=1, and C=?, then “(~A (B C))” = 23. If A=?, B=1, and C=0, then “((~A v ~B) C)” = 24. If A=1, B=?, and C=0, then “(A (~B ~C))” = 25. If A=?, B=1, and C=1, then “((A v B) v ~C)” = 26. If A=?, B=0, and C=1, then “(~A (~B ~C))” = 27. If A=?, B=0, and C=0, then “((A v B) v C)” = 28. If A=1, B=?, and C=1, then “((~A B) C)” = 29. If A=?, B=0, and C=1, then “((~A ~B) C)” = 30. If A=?, B=0, and C=1, then “(~A (B v C))” = 31. If A=0 and B=1, then “((A v B) ~A)” = 32. If A=1, B=0, and C=0, then “~((A B) v C)” = 33. If A=1 and B=1, then “(~(~A v ~B) v A)” = 34. If A=1, B=0, and C=0, then “(A (B C))” = 35. If A=1 and B=0, then “(A (B v A))” = 36. If A=1, B=0, and C=0, then “~(A (B ~C))” = 37. If A=1 and B=0, then “(~A v (B B))” = 38. If A=0 and B-1, then “~(~A (B A))” = 39. If A=1, B=0, and C=1, then “((A B) v C)” = 40. If A=1, B=1, and C=0, then “(~A v (B v C))” = Part III: Complete the following truth-tables. A B (A B) 0 0 0 1 1 0 1 1 A B (A B) 0 0 0 1 1 0 1 1 A B (A v B) 0 0 0 1 1 0 1 1 A B (B A) 0 0 0 1 1 0 1 1 A B ~(A B) 0 0 0 1 1 0 1 1 A B ~(A B) 0 0 0 1 1 0 1 1 A B (~A B) 0 0 0 1 1 0 1 1 A B ~(A v A) 0 0 0 1 1 0 1 1 A B ~(B v A) 0 0 0 1 1 0 1 1 A B ~(~A v (A B)) 0 0 0 1 1 0 1 1 A B C (A (B C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (~A v (B ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (A (~B v ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (A (B ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (A (B v C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (A v ~(B C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C ~(A v (~B ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C ~(~A ~(~B ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (A (B C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C ~(~A ~(~B ~C)) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Part IV: Determine whether the following arguments are valid or invalid using the truth-table method. A B ~(~A v B) A B 0 0 0 1 1 0 1 1 A B A ~B (~B ~A) 0 0 0 1 1 0 1 1 A B (A v B) ~B ~A 0 0 0 1 1 0 1 1 A B (A B) B A 0 0 0 1 1 0 1 1 A B ~(B B) ~A ~B 0 0 0 1 1 0 1 1 A B (B ~A) B (B v A) 0 0 0 1 1 0 1 1 A B ~A ~B (~A B) 0 0 0 1 1 0 1 1 A B ~(A v ~A) B ~(B v A) 0 0 0 1 1 0 1 1 A B (A (A v B)) B A 0 0 0 1 1 0 1 1 A B (A v B) (A B) (A B) 0 0 0 1 1 0 1 1 A B C ~((A v B) C) A ~C 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (~A (B C)) B A 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C ((A v B) v C) (B v A) C 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C ((~A v ~B) v ~C) ((A v B) v C) A 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C (~A B) ~(~A v C) (B