I am seriously lost with Proofs. I am allowed to use Rules of Inference (MP, MT, HS, Simp, AD, Conj, CD, and DS) and Rules of Equivalence (AB, Dem, Com, Assn, Dist, DN, Cont, MI, EX, ME, and RE)

 

Here are the ones I am working on right now. Any help would be greatly appreciated.

 

#15

1. (A∨B)∙(A∨G)

2. M→~A

3. ~Q→(~B∨~G) ∴ M→Q

#16

1. Y∙(~N∨A)

2. ~Y∨N

3. (A∙Y)→~~K ∴ K

#17

 

1. ~G→~F

2. (~F∨G)→(H∨J)

3. H→Z

4. J→~P ∴ P→Z

#18

1. (D∙E)∨(~D∙~E)

2. (H∙J)→~(D↔E)

3. ~~H∨J ∴ J↔~H

#19

1. (~E∨Z)∙(~E∨W)

2. ~K→E

3. ~K→(~Z∨~W)

4. K↔U ∴ R→U

#20

1. (R∙S)∨(R∙~E)

2. (Y∙O)→(E∙~S)

3. (O→~Y)→L ∴ L

#21

 

1. ~E

 

2. ~(E∙D)→F

3. (~F ∨ B)∙(~F∨C) ∴A∨(B∙C)

#22

1. T →R

 

2. R→S

3. ~R↔S ∴~T∙S

#23

 

1. (~K→K)→~L

 

2. ~(~L→~M)→L

3. M ∴ K↔~L

#24

1. W

2. ~Y→(~W∙~X) ∴ Y∙[(~W∙~X)→Z]

#25

1. F∨~I

2. I∨H

3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F

Edited June 24, 201213 yr by need help

Two things:

 

1) Are you allowed to use Condition Proof and Indirect Proof methods?

2) What have you tried so far? (we're not in the business of doing homework, but we'll help you get the answer yourself)

Two things:

 

1) Are you allowed to use Condition Proof and Indirect Proof methods?

2) What have you tried so far? (we're not in the business of doing homework, but we'll help you get the answer yourself)

 

1) We have not gotten to Condition Proofs yet that is next. Not sure what indirect proof method is.

 

2) That is exactly what I want. I want to learn it not have someone do it for me. I need guidance on what to do. If I have the rules I can figure it out or when I have the answers and have to figure out which rule applies but when I have to try to map it all and figure out what rules lead to what answers to get to the end I get lost. I just need some direction and hints on what I need to do.

1) We have not gotten to Condition Proofs yet that is next. Not sure what indirect proof method is.

 

2) That is exactly what I want. I want to learn it not have someone do it for me. I need guidance on what to do. If I have the rules I can figure it out or when I have the answers and have to figure out which rule applies but when I have to try to map it all and figure out what rules lead to what answers to get to the end I get lost. I just need some direction and hints on what I need to do.

 

We'll start with an easy one. Try number 16 and think double negation.

We'll start with an easy one. Try number 16 and think double negation.

 

 

4. (A∙Y)→K 3, DN [cond]

5. (Y∙~N)∨(Y∙A) 1, Dist [disj]

6. ~~(Y∙~N)∨(Y∙A) 5, DN [disj]

7. ~(~Y∨~~N)∨(Y∙A) 6, DeM [disj]

8. ~Y∨~~N 2, DN [disj]

9. ~~(~Y∨~~N) 8, DN [nega]

10. (Y∙A) 9,7, DS [conj]

11. (A∙Y) 10, Com [conj]

12. K 4,11, MP [atom]

Congratulations: No errors were found in the proof.

 

Edited June 24, 201213 yr by need help