Hi,

This is Question is for people who are skilled in their knowledge of logic!

I have attached a proof that uses the natural deduction style I would like you to use in your answer. If you do not understand this style PLEASE do not attempt my question. I do not want any de morgan's laws or equivalences used! I want the style shown in the provided proof.

My question is can you prove:

(p --> q) --> q |-- p v q

note: |-- represents "it follows"

--> represents "if then"

Please answer this question using the style in the sample proof provided. I have found no one who knows how to answer this yet. Thanks

(pa q) (r v S) E (p+ r) V (q S) > > > > 3, 4 1,5 AI E 7[] 8 VI -I 1 (1) (paq) (Irvs) 2 (2) -((pr) V (q- s) 3 (3) P 4 (4) 1 3,4 (5) paq 1,3,4 (6) rvs 7 (7) r 7 (8) pr 7 (9) (pr) V (q-s) 10 (10) s 10 (11) q?s 10 (12) (pr) V (q + S) 1,3,4 (13) (pr) V (q + s) 1,2,3,4 (14) --s 1,2,3,4 (15) s 1,2,3 (16) 1s 1,2,3 (17) (pr") v (q + s) 1,2,3 (18) var 1,2,3 (19) r 1,2 (20) P+r 1,2 (21) (p 1) V (q+s) 1 (22) --((p r) V (q- s) 1 (23) (pr) V (q-s) 10 [] ?I 11 VI 6, 9 [7], 12 [10] VE 2, 13 [] RAA 14 --E 15 [4] SI 16 VI 2, 17 [] RAA 18 --E 19 [3] +I 20 VI 2, 21 [2] RAA 22 G-E (pa q) (r v S) E (p+ r) V (q S) > > > > 3, 4 1,5 AI E 7[] 8 VI -I 1 (1) (paq) (Irvs) 2 (2) -((pr) V (q- s) 3 (3) P 4 (4) 1 3,4 (5) paq 1,3,4 (6) rvs 7 (7) r 7 (8) pr 7 (9) (pr) V (q-s) 10 (10) s 10 (11) q?s 10 (12) (pr) V (q + S) 1,3,4 (13) (pr) V (q + s) 1,2,3,4 (14) --s 1,2,3,4 (15) s 1,2,3 (16) 1s 1,2,3 (17) (pr") v (q + s) 1,2,3 (18) var 1,2,3 (19) r 1,2 (20) P+r 1,2 (21) (p 1) V (q+s) 1 (22) --((p r) V (q- s) 1 (23) (pr) V (q-s) 10 [] ?I 11 VI 6, 9 [7], 12 [10] VE 2, 13 [] RAA 14 --E 15 [4] SI 16 VI 2, 17 [] RAA 18 --E 19 [3] +I 20 VI 2, 21 [2] RAA 22 G-E