SOLUTION: <pre> Give reasons for the steps, given premises 1, 2 and 3: 1. X &#8835; (Y &#8835; Z) 2. X &#8835; (A &#8835; B) 3. X • (Y &#8744; A) &#8756; &#8764;B &#8835; X

Algebra ->  Proofs -> SOLUTION: <pre> Give reasons for the steps, given premises 1, 2 and 3: 1. X &#8835; (Y &#8835; Z) 2. X &#8835; (A &#8835; B) 3. X • (Y &#8744; A) &#8756; &#8764;B &#8835; X      Log On


   

Question 1116905: 
Give reasons for the steps, given premises 1, 2 and 3:

1.  X ⊃ (Y ⊃ Z)

2.  X ⊃ (A ⊃ B)

3.  X • (Y ∨ A)     ∴  ∼B ⊃ X 

4.  X                   

5.  A ⊃ B          

6.  Y ⊃ Z           

7.  (Y ∨ A) • X    

8.  Y ∨ A              

9. ∼(∼Y) ∨ A       

10. ∼Y ⊃ A          

11. ∼Y ⊃ B         

12. ∼B ⊃ ∼(∼Y)  

13. ∼B ⊃ Y          

14.  X ∨ ∼Y         

15.  ∼Y ∨ X        

16.  Y ⊃ X           

17. ∼B ⊃ X

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Give reasons for the steps, given premises 1, 2 and 3:

1.  X ⊃ (Y ⊃ Z)

2.  X ⊃ (A ⊃ B)

3.  X • (Y ∨ A)     /∴  ∼B ⊃ X 

4.  X                 3, Simplification

5.  A ⊃ B           2,4, Modus Ponens

6.  Y ⊃ Z           1,4, Modus Ponens

7.  (Y ∨ A) • X       3, Commutation

8.  Y ∨ A             7, Simplification 

9. ∼(∼Y) ∨ A          8, Double Negation

10. ∼Y ⊃ A           10, Material Implication

11. ∼Y ⊃ B         10,5, Hypothetical Syllogism

12. ∼B ⊃ ∼(∼Y)       11, Transposition

13. ∼B ⊃ Y          12, Double Negation

14.  X ∨ ∼Y           4, Addition

15.  ∼Y ∨ X          14, Commutation

16.  Y ⊃ X           15, Material Implication

17. ∼B ⊃ X        13,16, Hypothetical syllogism

Edwin