PHIL 206: Deductive Logic

Larkin: Fall 2003

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Test #2: Truth Table Analysis

Review

I. Section 7.3

Part B

2. Invalid: F = f, G = t

3. Valid

5. Invalid: A =f, B = t

6. Invalid: X = t, Y = t

8. Valid

9. Invalid: F = f, G = t ( or F = t, G = f)

11.Valid

12. Valid

13. Valid

14. Invalid: B = t, S = f, H = t

15. Valid

16. Invalid: S = f, Z = t, G = t

17. Valid

18. Valid

19. Valid

20. Valid

Part C

2. (M v G) ® H, G /\ H Valid

3. B v M, ~M « N, N /\ B Valid

5. ~N® ~C, ~C ® ~V, V /\ N Valid

6. L ® (B v S), ~S · L /\ B Valid

8. V ® A, ~V ® H, ~A ® ~H /\ Valid

9. L ® N, ~P ® ~N, ~P /\ ~L Valid

10. H ® E, ~E v ~V, V /\ ~H Valid

II. Section 7.4

Part C

2. Invalid G = T, F = F, H = F

3. Valid M = F

[only way to make premise true forces conclusion true]

5. Valid Q = T, P = T, R = T

[making conclusion false and second premise true forces first premise to be false]

6. Valid Z = F, Y = F, X = F

[only way to make all premises true]

7. Invalid W = T, J = T, R = F, S = T

8. Valid P = F, O = F, N = T, M = T

[only way to make all premises true]

9. Invalid A = F, B = T, C = T

10. Invalid P = T, Q = T, R = F

Part D

2. Done in class

3. (F ® S) · F /\ (N « ~S) ® ~N Valid

5. Done in class

6. V ® E, ~V ® D, ~E ® ~D /\ D Invalid

[D = F, V = T, E = T]

8. E v S, E ® (B · U), ~S v ~U /\ B Invalid

[B = F, E = F, S = T, U = F]

9. E ® W, E « V, V ® R, R ® C /\ W ® C Invalid

[W = T, C = F, R = F, V = F, E = F]

10. W « P, M « L, ~(L · P) /\ ~(W v M) Invalid

[W = T, P = T, M = F, L = F]

III. Section 7.5

Part C

2. W · P, W ® ~P /\ M Valid

[premises are contradictory, so cannot all be true—if you make the first premise true, it forces the second premise to be false]

3. U v ~U /\ T Invalid

[T = F, U = T/F]

5. W ® (R ® W) /\ S v ~S Valid

[conclusion cannot be false, so cannot have all true premises and a false conclusion]

6. D ® ~F, D · F /\ L Valid

[same deal as #2]

7. B ® C /\ B ® C Valid

[obviously if make conclusion false, it automatically makes the premise false]

8. ~(E · ~E) /\ E Invalid

[ E = F]

9. U ® (L « ~L) /\ ~U Valid

[only way to make conclusion false makes the premise false also—for, no matter L is, ‘L «~L’ is false]

10. ~A ® ~L, A « C, L · ~C /\ ~L Valid

[again the premises here are inconsistent—if we make third and first premises both true, then second premise forced to be false]