Solutions to Fill in the Blank Exercises

Using MP, MT, HS, DS, CD, SM, CN, AD, CM, AS, and DN, see if you can draw inferences allowed by the rules, given these premises.

 

a.

1. (D v M) ⊃ T

2. ~T

3. __ ~(D vM)____ __1,2 _MT___

 

b.

1. (P ≡ (U v I)) v (B ∙ N)

2. ~ (P ≡ (U v I))

3. __B ∙ N_____ __1,2 DS____

 

c.

1. M ⊃ (P ∙ L)

2. (G ⊃ I) ⊃ M

3. ___(G ⊃ I) ⊃ (P ∙ L)__1,2___ _HS____

 

d.

1. E ⊃ (Y ⊃ U)

2. (E ⊃ (Y ⊃ U)) ⊃ (C v (G ∙ M)

3. __C v (G ∙ M)_______ _1,2 MP_____

 

e.

1. B v Y

2. V ⊃ O

3. _(B v Y) ∙ (V ⊃ O)____1,2___ CN _____

 

f.

1. P ∙ (I ⊃ L)

2. T ⊃ C

3. __ P_____ __ 1 SM____

 

g.

1. P ∙ (I ⊃ L)

2. T ⊃ C

3. _(I ⊃ L) ∙ P_____ _1, CM____

4. I ⊃ L 3 SM

 

h.

1. L v (C ∙ G)

2. (L ⊃ S) ∙ ((C ∙ G) ⊃ (T ≡ R))

3. ____S v (T ≡ R)___1,2 __ CD _______

 

i.

1. ~(C ∙ G) ⊃ (T ≡ R)

2. ~ (T ≡ R)

3. ___~~(C ∙ G)___1 , 2_ ____MT

4. __ C ∙ G __ 3 DN_

 

j.

1. ((N v (J v L)) ⊃ T

2. ~ T

3. __~((N v (J v L)__1_ _MT__

4. ~((N v J) v L) 3, AS

 

k.

1. F ⊃ (P v C)

2. (B ∙ C) ⊃ F

3. ~(C v P)

4. __(B ∙ C) ⊃ (P v C) 1,2 ___ HS ___

5.___~(P v C)__ 3 CM___

6. ~(B ∙ C) ___4, 5 MT_____

 

l.

1. T ⊃ (I ∙ O)

2. (W v (B v T)

3. ~(W v B)

4. _ (W v B) v T____2__ AS ______

5. ____T____ ___3,4 DS___

6. ____I ∙ O____ __1,5 MP____

7. I ___6 SM____

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