A.
1. (P -> -F)
2. [(S v M) & P]
3. (E -> {(T & -O) -> [(R & (A v H)]}) [Note: 'since' is used here as a conditional]
4. (O -> J)
5. [(S & -E) -> O]
6. [(E v S) -> C]
7. {(-G & L) -> [(P & U) v (S & T)]}
8. [(A -> L) & -(L -> A)]
9. (C <-> J)
10. [-R & (A & -B)]
11. {(P v C) v [R & (N & -I)]}
12. (-B v V)
13. (P <-> T)
14. [(R v S) & -(R & S)]
15. [R -> (H v J)]
16. [(W v -W) & -(W & -W)]
17. -R
18. [-R -> (-J -> K)]
19. [M & (F v G)]
20. {(P -> E) v [(B -> P) & -(B -> E)]}
B.
1. If Shakespeare and Galileo were both born in 1564, then they were contemporaries.
2. If Ptolemy was the father of astronomy, then if Ptolemy was contradicted by Copernicus, then Copernicus held a heliocentric theory.
3. Either Ptolemy or Copernicus was the father of astronomy.
4. Galileo having contradicted himself is neither a necessary nor a sufficient condition for his works being full of important philosophical insights.
5. If Brahe rejected the Copernican theory, then Kepler didn't admire Brahe.
6. Brahe rejected the Copernican theory, and if Copernicus held a heliocentric theory, then Kepler wasn't Brahe’s assistant.
7. Galileo either proved Aristotle wrong about planetary motion or he didn't; but he didn’t both prove Aristotle wrong and not prove him wrong.
8. Either Copernicus or Ptolemy was the father of astronomy, unless Ptolemy was contradicted by Copernicus.
9. It is false that Ptolemy was the father of astronomy, and that both Copernicus held a heliocentric theory and Ptolemy was contradicted by Copernicus.
10. If Copernicus was the father of astronomy, then if he held a heliocentric theory, then neither was Ptolemy the father of astronomy nor did Kepler admire Brahe.
11. Either Ptolemy wasn't contradicted by Copernicus or Kepler's third law isn't still in use today.
12. It is not the case both that Galileo proved Aristotle wrong about planetary motion and Galileo contradicted himself, and that Galileo’s works are full of important
philosophical insights.
13. Copernicus’ holding a heliocentric theory implies that he was the father of astronomy and Galileo proving Aristotle wrong about planetary motion implies that Copernicus wasn't the
father of astronomy.
14. It is false that Kepler being Brahe's assistant implies that Kepler's third law is still in use today.
15. If Brahe’s having rejected the Copernican theory implies that Copernicus held a heliocentric theory, then Ptolemy was not contradicted by Copernicus.
C.
True: 5, 8, 11, 13, 14, 15.
False: 1, 2, 3, 4, 6, 7, 9, 10, 12.
4.2.A.
1. Negated Disjunction
2. Conditional
3. Disjunction
4. Disjunction
5. Disjunction
6. Conjunction
7. Negated Conditional
8. Doubly Negated Biconditional
9. Conditional
10. Biconditional
11. Negated Conditional
12. Negated Conjunction
13. Disjunction
14. Negated Disjunction
15. Conditional
16. Disjunction
17. Conditional
18. Disjunction
19. Conditional
20. Negated Biconditional
4.2.B.
1. Truth value cannot be determined just by using the truth table method. Without knowing the actual truth value of M, we cannot determine the truth value of this sentence. If M is true, the sentence is false; if M is false, the sentence is true.
2. Cannot be determined. Need to know the actual value of L here to determine the truth value of the sentence.
3. Cannot be determined. Need to know the actual value of L here to determine the truth value of the sentence.
4. This sentence is true, when K is false, no matter what the values are of M and N.
5. This sentence is false, no matter what the value is of M.
6. This sentence is false.
7. Cannot be determined with knowing actual values of are L, M, and N.
8. This sentence is false.
9. Cannot be determined without knowing the values are of L and N.
10. This sentence is true.
11. This sentence is true, no matter what the value is of J.
12. This sentence is false, no matter what the value is of J.
13. This sentence is true.
14. Cannot be determined without knowing the values are of M and N.
15. This sentence is false, no matter what the values are of M and N.
16. This sentence is false.
17. This sentence is true, no matter what the value is of D. Note that D does not appear in the translation dictionary. This is an error; D should have been replaced by N.
18. This sentence is false.
19. This sentence is true.
20. This sentence is true, no matter what the values are of L and N.
21. This sentence is true, no matter what the value is of L.
22. This sentence is true.
23. This sentence is true, no matter what the value is of M.
24. The truth value of this sentence cannot be determined without knowing the actual truth values of L and M.
25. This sentence is true.
4.3.A. Page 98.
L-true: 2, 5, 7, 8, 15, 17, 19.
L-false: 6, 9, 10, 16, 18.
L-indeterminate: 1, 3, 4, 11, 12, 13, 14, 20.
4.3.B. Page 98.
1. Incompatible
2. Equivalent
3. Incompatible
4. Incompatible
5. Incompatible
6. Incompatible
7. Contradictory
8. Incompatible
9. Incompatible
10. Incompatible
11. Equivalent
12. Incompatible
13. Equivalent
14. Incompatible
15. Contradictory
16. Equivalent
17. Incompatible
18. Incompatible
19. Contradictory
20. Incompatible
4.3.C. Page 99
True: 3, 5, 9, 10.
False: 1, 2, 4, 6, 7, 8.
Last updated: 9 July 2015