logic homework help

2.)
* 1. T v P a.
* 2. P--> S a.
** 3. ~T a. (for i -->)

(first lemma)
*** 4. T a. (for elimination v)
**** 5. ~S a.
**** 6. T & ~T i &/3,4
*** 7. ~~S i ~/ 5-6
*** 8. S e ~/7

(second lemma)
*** 9. P a. (for elimination v)
*** 10. S e -->/2,9

**11. S e v/1, 4-8, 9-10
*12. ~T --> S i -->/3-11

5.)

*1. P v (S & R).........................a.
*2. T --> (~P & ~R) ................a.
**3. T.....................................a. (for reductio)
**4. (~P & ~R).......................2,3/e -->

(first lemma)
***5. P..................................a.
***6. ~P...............................4/e &
***7. contradiction...............5-6/ i contradiction

(second lemma)
***8. S & R............................a.
***9. R..................................8/e &
***10. ~R..............................4/e &
***11. contradiction..............9-10/ i contradiction

**12. contradiction ................1, 5-7 (first lemma), 8-11 (second lemma)/ e v
*13. ~T...................................3-11/ i ~

1. T v P
2. P --> S /.:~T-->S

3. ~T>P (From 1. material imp.)
4. ~T>S (From 3 and 2. hypothetical syllogism).