Question 1116905
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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 

4.  X                 3, Simplification

5.  A &#8835; B           2,4, Modus Ponens

6.  Y &#8835; Z           1,4, Modus Ponens

7.  (Y &#8744; A) • X       3, Commutation

8.  Y &#8744; A             7, Simplification 

9. &#8764;(&#8764;Y) &#8744; A          8, Double Negation

10. &#8764;Y &#8835; A           10, Material Implication

11. &#8764;Y &#8835; B         10,5, Hypothetical Syllogism

12. &#8764;B &#8835; &#8764;(&#8764;Y)       11, Transposition

13. &#8764;B &#8835; Y          12, Double Negation

14.  X &#8744; &#8764;Y           4, Addition

15.  &#8764;Y &#8744; X          14, Commutation

16.  Y &#8835; X           15, Material Implication

17. &#8764;B &#8835; X        13,16, Hypothetical syllogism

Edwin</pre>