L o g i c

Solutions to Ch. 6


Text: First Logic, 3/e, by Michael F. Goodman.



6.A. Page 137
Valid: 1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 18.
Invalid: 3, 8, 11, 14, 15, 16, 17, 19, 20.

6.B. Page 138

L-true: 2, 5, 21, 22, 23.
L-false: 10, 12, 14, 16, 26, 28.
L-indeterminate: 1, 3, 4, 6, 7, 8, 9, 11, 13, 15, 17, 18, 20, 24, 25, 27, 29. 30.

6.C. Pages 138-141 (Note: '&' is used for the dot; '//' separates premises; '|-' is the conclusion indicator)

1. (A <-> R) // R    |- (A -> C) (Invalid)

2. (P -> L) // (L -> S)    |- (S v -P) (Valid)

3. (T -> -R) // (D -> -A) // (-D -> P)    |- (R -> -A) (Invalid)

4. (S v H) // (-G -> -S)    |- (H -> G) (Invalid)

5. See the book, page 234.

6. [(J & E) -> -C] // (E -> C) // -E     |- (-E & -J) (Invalid)

7. (G v U) // [(M -> G) & (-M -> U)] // -M     |- -G (Invalid)

8. (B -> R) // [-(R & M) -> B]    |- R (Valid)

9. (R -> G) // (A -> I) // [M -> (R v A)] // M     |- (G v -I) (Invalid)

10. See the book, page 234.

11. [(L & G) -> (-P v W)] // [(P v I) -> L] // [(P v E) -> G] // (P & J)     |- W (Valid)

12. (L -> P) // (R -> L) // (B -> -L) // (P -> D)     |- -L (Invalid)

13. (F -> T) // (T -> P) // -P // (W -> F) // (W v F)     |- (P v P) (Valid)

14. (R -> A) // [(H & W) -> R] // (A -> B) // -B //    |- (-H v –W) (Valid)

15. See the book, page 234.

16. (A -> G) // (G -> U) // (A v G)     |- [(A v U) & (A -> U)] (Valid)

17. There are two arguments here. Argument #1 is presented in the first sentence, where 'since' is the premise indicator. First arg: T     |- (P -> D) (Invalid)

17. Second arg: (P -> D) // [(R v C) -P] // (C & -S)    |- D (Valid) [Note here that I used the conclusion of the first arg as the first premise of the second arg.]

18. [(C & P) v (C & S)] // [(C v N) -> L]     |- L (Valid)

19. [(S -> F) v (M & W)] // -(M & W) // -F    |- -S (Valid)

20. See the book, page 234.



Michael F. Goodman
Department of Philosophy
Humboldt State University