including line numbers and rules:

Each of the following is a formal proof of validity for the indicated argument. State the justification for each numbered line that is not a premise. Indicate which lines respond to the justification

(5 Points Each)

A.    1)  (L  É  M)  É  (N  º  O)

2) (P  É  ~Q)  É  (M  º  ~Q)

3) {[(P  É  ~Q)  v  (R  º  S)]  ·  (N  v  O)}  É  [(R  º  S)  É  (L  É  M)]

4) (P  É  ~Q)  v  (R  º  S)

5)  N  v  O

\ (M  º  ~Q)  v  (N  º  O)

6) [(P  É  ~Q)  v  (R  º  S)]  ·  (N  v  O)  1,2 SIMP

7)  (R  º  S)  É  (L  É  M)

8) (R  º  S)  É  (N  º  O)

9) [(P  É  ~Q)  É  (M  º  ~Q)]  ·  [(R  º  S)  É  (N  º  O)]

10) (M  º  ~Q)  v  (N  ºO)

B.    1) R  v  ~(P  ·  Q)

2) (~E  ·  ~R)  É  (B  ·  A)

3) E  É  (P  ·  Q)

4­) ~R

\ B  v  (F  ·  G)

5) ~(P  ·  Q)

6) ~E

7) ~E  ·  ~R

8) B  ·  A

9) B

10) B  v  (F  ·  G)

Construct a proof of validity for the following arguments, including line numbers and rules:

(5 POINTS)

C.    1) F  É  ~G

2) ~F  É  (H  É ~G)

3)  (~I  v  ~H)  É  ~ ~ G

4)  ~I

\ ~H

5)

(5 POINTS)

D.    1. ~A כ  [A v (T כ R)]

2. ~R  כ [R v (A כ R)]

3. (T v D) כ ~R

4. T v D

5. ~R

\  D

Translate the following argument into symbolic form and use the 9 rules of inference to proof the argument.

(5 POINTS)

E.     If terrorists take more hostages, then the terrorist demands will be met if and only if the media give full coverage to terrorist acts. Either the media will voluntarily limit the flow of information or if the media will recognize they are being exploited by terrorists, they will voluntarily limit the flow of information. Either the media will recognize they are being exploited by terrorists or terrorists will take more hostages. The media will not voluntarily limit the flow of information. Therefore, terrorist demands will be met if and only if the media give full coverage to terrorist acts. (H, D, A, V, R)

F.     If either parents get involved in their children’s education or the school year is lengthened, then if the children learn phonics, their reading will improve and if they are introduced to abstract concepts earlier, their math will improve. If either parents get involved in their children’s education or nebulous subjects are dropped from the curriculum, then either the children will learn phonics or they will be introduced to abstract earlier. Parents will get involved in their children’s education, and writing lessons will be integrated with other subjects. Therefore, either the children’s reading or their math will improve. (P, S, L, R, I, M, N, W).