Symbolic Logic 5E: 3.4

“Give conditional proofs of validity for Exercises 21*, 22, 23, 24, and 25 on pages 47-48.”

21. In back of book.

22.

  1. (T→E) ∧ (A→L) …Therefore, (T ∧ A)→(E ∧ L)
  2. T ∧ A (CP)
  3. T (2,SIMP)
  4. T→E (1,SIMP)
  5. E (3,4,MP)
  6. A→L (1,SIMP)
  7. A (2,SIMP)
  8. L (7,6,MP)
  9. E ∧ L (5,8,CONJ)
  10. (T ∧ A)→(E ∧ L) (2-9,CP)

23.

  1. E→S
  2. E→(S→N)
  3. S→(N→F) …Therefore, E→F
  4. E (CP)
  5. S (4,1,MP)
  6. S→N (2,4,MP)
  7. N (5,6,MP)
  8. N→F (5,3,MP)
  9. F (7,8,MP)
  10. E→F (4-9,CP)

24.

  1. A→(B ∨ C)
  2. E→(C ∨ P)
  3. ¬C …Therefore, ¬(B ∨ P)→¬(A ∨ E)
  4. ¬(B ∨ P) (CP)
  5. ¬B ∧ ¬P (4,DeM)
  6. ¬B (5,SIMP)
  7. ¬B ∧ ¬C (6,3,CONJ)
  8. ¬(B ∨ C) (7,DeM)
  9. ¬A (8,1,MT)
  10. ¬P (5,SIMP)
  11. ¬P ∧ ¬C (3,9,CONJ)
  12. ¬(E ∨ P) (11,DeM)
  13. ¬E (12,2,MT)
  14. ¬A ∧ ¬E (9,13,CONJ)
  15. ¬(A ∨ E) (14,DeM)
  16. ¬(B ∨ P)→¬(A ∨ E) (4-15,CP)
Advertisements

Leave a comment

Filed under Solution Sets

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s