Sunday, 20 June 2021

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 7.7, 12, p. 390

Prove the logical truth.

 

1.     ⊃ (Q ⊃ R)

2.     Q

3.     P

4.     ⊃ R

5.     R

6.     ⊃ R

7.     ⊃ (P ⊃ R)

8.     [P ⊃ (Q ⊃ R)] ⊃ [⊃ (P ⊃ R)]

9.     ⊃ (P ⊃ R)

10.  P

11.  Q

12.  ⊃ R

13.  R

14.  ⊃ R

15.  ⊃ (Q ⊃ R)

16.  [⊃ (P ⊃ R)] ⊃ [⊃ (Q ⊃ R)]

17.  {[P ⊃ (Q ⊃ R)] ⊃ [⊃ (P ⊃ R)]} • {[⊃ (P ⊃ R)] ⊃ [⊃ (Q ⊃ R)]}

18.  [P ⊃ (Q ⊃ R)] ≡ [Q ⊃ (P ⊃ R)]

/ [P ⊃ (Q ⊃ R)] ≡ [Q ⊃ (P ⊃ R)]

ACP

ACP

ACP

1,2 MP

2,4 MP

3-5 CP

2-6 CP

1-7 CP

CP

CP

CP

9,11 MP

10,12 MP

11-13 CP

10-14 CP

 

9-15 CP

8-16 Conj

17 Equiv

No comments:

Post a Comment