True: 1, 3, 5, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20.
False: 2, 7, 8, 9, 12, 17.
Ambiguous: 6. The sentence doesn't refer to the number of different sentence components. If there are five different sentence components in the sentence, then this sentence is true.
5.1.B. Page 105
Valid: 1, 3, 5, 6, 8, 9, 10, 14, 15, 16, 17, 20.
Invalid: 2, 4, 7, 11, 12, 13, 18, 19.
5.1.C. Pages 105-107
1. Invalid: (U -> G) (I -> G) |- (-U v I)
2. Invalid: -(W <-> J) |- (-J -> -W)
3. Valid: -(D -> P) -(P -> M) |- -(D -> M)
4. The translations of the second premise and the conclusion are not possible with just the tools we have in our present system. We cannot adequately translate 'it is better than' and 'all right' in our system. Need a higher level logic to do that, which adds more symbols.
5. Invalid: [-O -> (G & C)] [(O & H) -> P] (O & J) |- S [Note: '&' used for conjunctions]
6. Invalid: {[(L & P) & S] -> -H} -S |- H
7. Valid: (J v S) -(J & S) (S -> C) (-J -> -C) -J |- (S & -C)
8. Valid: (R -> S) (S -> N) (R & -N) |- S
9. Invalid: [-S v (Ci & Ca)] [(W & C) -> Cs] |- [S -> (W & C)]
10. Invalid: [(-C & B) -> O] [-O -> (C -> E)] (-E v H) -H |- O
11. Need a good translation here. Still contemplating.
12. Valid: [(G -> H) & (P -> S)] (-S & G) |- (-P & H)
13. Invalid: {C -> [(T & F) & (Q & P)] [(T & F) & (Q & P)] |- C
14. Valid: [(J & A) -> (P -> T)] (S -> L) [(T & S) & (A & B)] |- L
15. Valid: (S v -T) (-P & - - T) |- S
5.2. Page 113
Valid: 1, 2, 5, 6, 7, 8, 9, 11, 12, 16, 20.
Invalid: 3, 4, 10, 13, 14, 15, 17, 18, 19.