# Solutions to Pattern Recognition exercise

In the following set of examples, focus on the main operators of the premises, and see which rules are being exemplified. Do not be concerned about the order in which you find the premises, that really makes no difference.

1. C ⊃ B / A ⊃ C // A ⊃ B

HS

p⊃q

q⊃r

/ p⊃r

2. (F ∙ N) ⊃ (L v M) / ~ (L v M) // ~ (F ∙ N)

MT

p ⊃ q

~q

/ ~p

3. ((G ⊃ V) ∙ L) // G ⊃ V

SM

p ∙ q

/p

4. (D ⊃ ( I ∙ O)) ∙ (( P v M) ⊃ L) / D v (P v M)

// (I ∙ O) v L

CD

(p⊃q) ∙ (r⊃s)

p v r

/ q v s

5. (G ⊃ (M ⊃ U)) ⊃ O / G ⊃ (M ⊃ U) // O

MP

p⊃q

p

/q

6. ~(N v L) > ( P ∙ L) / ~ (P ∙ L) // ~ ~(N v L)

MT

7. (B ∙ P) v (H ⊃ I) // ((B ∙ P) v (H ⊃ I)) v (L v (F ∙ ~E))

p

/ p v q

In this next set, a premise will be missing, but a conclusion is proposed. See if you can tell what the missing premise is, and what the rule is, that will make the conclusion follow in each case:

8. (H ∙ E) ⊃ (G v L) / _H ∙ E___________ // G v L

MP

9. (J ≡ (B ∙ V)) v (F ⊃ (V v C)) / _~(J ≡ (B ∙ V)_

// F ⊃ (V v C)

DS

10. {(M ∙ A) ⊃ [(R v T) ∙ (I v N)]} ∙ [H ⊃ (E ∙ I)] / __(M ∙ A) v H____ // [(R v T) ∙ (I v N)] v (E ∙ I)

CD

p = (M . A)

q= [(R v T) . (I v N)]

r = H

s = (E . I)

(p ⊃ q) ∙ (r ⊃ s) / p v r // q v s

11. (S ∙ (A v R)) ⊃ [T v (R ∙ E)] / _~[T v (R ∙ E)_ // ~ (S ∙ (A v R))

MT

12. (K v A) / __N ⊃ T____ // ((K v A) ∙ (N ⊃ T))

CN

13. H ⊃ (U ⊃ (M v E)) / __(U ⊃ (M v E) ⊃ (R ⊃ D)__ // H ⊃ (R ⊃ D)

HS

p = H

q = (U ⊃ (M v E))

r = (R ⊃ D)

14. H ⊃ (U ⊃ (M ∙ E) / ____H________________ // (U ⊃ (M ∙ E)

MP

15. (Q ∙ U) ⊃ [(I ≡ N) ⊃ E] / ____~[(I ≡ N) ⊃ E____

// ~( Q ∙ U)

MT