Reference no: EM13762214

Part A: Abbreviated Truth Tables Use abbreviated truth tables to show that the following arguments are invalid.

3.~(G↔H) ∴ ~G→~H

 

4.J→~K ∴ ~(J↔K)

 

8.(F·G)↔H, ~H ∴ ~G

 

9.~(B→C), (D·C)∨E ∴ ~B

 

14.~(C∨D), (~C·~E)↔~D, ~E→(C∨F), S∨F ∴ S

 

17.S→(A·O), ~P∨~R, P→(S∨Z), Z→(O→R) ∴ Z∨~P

 

18.A∨(B·C), ~A ∴ (A·B)∨(A·C)

 

20.~J·~K, L→J, M→K, (M→~L)→~(N·O) ∴ ~N

 

 

 

Part B: More Abbreviated Truth Tables Use abbreviated truth tables to show that the following arguments are invalid.

2.L↔(M·N), M∨N, ~L ∴ ~M

 

3.(O↔P)→R, ~R ∴ ~O∨P

 

5.~(Z·H), ~Z→Y, W→H ∴ ~W→Y

 

6.~X∨(C·A), ~Y∨~B, ~Y∨(X∨T), T→(A→B) ∴ T∨~Y

 

8.B→(C·D), ~E∨~F, E→(B∨G), G→(D→F) ∴ G∨~E

 

9.~(D↔E), ~D→F, E→G ∴ F·G

 

11.~[(J·K)→(M∨N)] ∴ K·N

 

12.A→B, C→~D, ~B∨D ∴ ~A↔~C

 

13.~E→(G·A), ~(P↔~L)∨E, ~(P·L)∨Q, ~N→~G ∴ Q·A

 

14.(G→E)↔S, ~(S∨H), ~(P·~H) ∴ G·E

 

15.~(C↔~D)∨E, ~E→(G·H), (C·D)→K, ~N→~G ∴ K·H

 

Part C. Still More Abbreviated Truth Tables Use abbreviated truth tables to show that the following arguments are valid.

1.H → ~B, D → B, H ∴ ~D

 

2.F → (G → H), ~F → J, ~(G → H) ∴ J

 

3.(F ∨ E) → ~D, S ∨ D, E ∴ S

 

5.(A · E) → F, E, F → (D · ~C), A ∴ ~C

 

6.~F ∨ ~G, ~F → Z, ~G → ~R, (Z ∨ ~R) → (U → P), ~P ∴ ~U

 

7.C → (T → L), ~L, ~E → C, L ∨ ~E ∴ ~T

 

8.~~A, B → ~A ∴ ~B

 

9.(B · A) → C, ~D → (B · A), ~C ∴ ~~D

 

11.(G ∨ H) → (J ∨ K) ∴ ~(J ∨ K) → ~(H ∨ G)

 

12.(M ∨ N) → ~S, T → (M ∨ N), ~S → ~(M ∨ N) ∴ T → ~(M ∨ N)

 

13.X ↔ Y, ~~(X ∨ Y) ∴ X · Y

 

15.~F, ~(F · ~S) → ~P, (~S · F) ∨ ~T ∴ ~(P ∨ T)

 

 

Part C: Valid or Invalid? Some of the following arguments are valid, and some are invalid. Use abbreviated truth tables to determine which are valid, and which are invalid.

2.F→(G↔H), ~F·~H ∴ ~G

 

3.~M ∴ (~N∨~M)

 

5.P→~(Q·R), P·R ∴ ~Q

 

6.X→Z, Y→Z, ~Z ∴ X↔Y

 

7.~(S→R), S→J, ~R↔W ∴ W→~J

 

8.~M→O, ~N→O, ~O↔~P, ~P ∴ M·N

 

9.(A∨B)·(A∨C) ∴ A·(B∨C)

 

10.R↔~Q, R∨Q, R∨P ∴ (P·Q)→R