SOLUTION: Can anyone annotate the following proofs for me? Proof 1: 1. (AvB) -> C 2. (CvD) -> E 3. CvA 4. ~C .: E 5. A 6. AvB 7. C 8. CvD 9. E Proof 2 1. X->Y

Algebra ->  Proofs -> SOLUTION: Can anyone annotate the following proofs for me? Proof 1: 1. (AvB) -> C 2. (CvD) -> E 3. CvA 4. ~C .: E 5. A 6. AvB 7. C 8. CvD 9. E Proof 2 1. X->Y      Log On


   

Question 929923: Can anyone annotate the following proofs for me?
Proof 1:
1. (AvB) -> C
2. (CvD) -> E
3. CvA
4. ~C .: E
5. A
6. AvB
7. C
8. CvD
9. E

Proof 2
1. X->Y
2. X->Z .: X-> (Y&Z)
3. ~XvY
4. ~XvZ
5. (~XvY) & (~XvZ)
6. ~Xv(Y&Z)
7. X-> (Y&Z)
Proof 3
1. ~(A&(BvC)) .: A -> ~B
2. ~((A&B)v(A&C))
3. ~(A&B) & ~(A&C)
4. ~(A&B)
5. ~A v ~B
6. A -> ~B
PLEASE and thank you!!!! I need lines and rules.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
 
1. (AvB) -> C
2. (CvD) -> E
3. CvA
4. ~C       
       .: E  
5. A            3,4,DS      (disjunctive syllogism) 
6. AvB          5,addition  (disjunctive addition)  
7. C            1,6,MP      (modus ponens)
8. CvD          7,addition  (disjunctive addition)
9. E            2,8,MP      (modus ponens) 

----------------------------

1. X->Y
2. X->Z
    .: X->(Y&Z)
3. ~XvY           1,writing a conditional 
                    as a disjunction
4. ~XvZ           2,writing a conditional
                    as a disjunction 
5. (~XvY)&(~XvZ)  3,4,conjunction 
6. ~Xv(Y&Z)       5,distributive   [" taking out ~Xv "]
7. X->(Y&Z)       6,writing a disjunction as 
                    a conditional

-----------------------------

1. ~(A&(BvC)) .: A->~B
2. ~((A&B)v(A&C))        1, distributive
3. ~(A&B)&~(A&C)         2, deMorgan's 
4. ~(A&B)                3, simplification 
5. ~Av~B                 4, deMorgan's law
6. A->~B                 5,writing disjunction 
                           as a conditional

Edwin