MHB How Do I Apply Natural Deduction to These Logic Problems?

[TremblayFil]

Hello guys,

I really need help from you about natural deduction. I just can't get to solve theses problems. Can anyone give me the solutions ? I've been trying for hours... Thanks a lot !

Premise 1 : B,
Premise 2 : C→(¬B∨A)
Premise 3: ¬C→¬(A∨B)
Conclusion : A≡C

____

Premise 1: (A∨B)∨C
Premise 2 : ¬B∧¬C
Conclusion : A

____

Premise : ¬(A ∨ B)
Conclusion : ¬A ∧ ¬B

_____

Premise : ¬A ∧ ¬B
Conclusion : ¬(A ∨ B)
Thank you so much !

 

[MarkFL]

Hello, and welcome to MHB, TremblayFil! (Wave)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Also, and just for future reference, we ask that no more than 2 questions be posted per opening post. Follow-up questions regarding those problems initially posted are of course allowed, and even encouraged, but threads with a long list of questions can become convoluted and hard to follow.

Can you post what you have done so far?

 

[solakis1]

Hello guys,

I really need help from you about natural deduction. I just can't get to solve theses problems. Can anyone give me the solutions ? I've been trying for hours... Thanks a lot !

Premise 1 : B,
Premise 2 : C→(¬B∨A)
Premise 3: ¬C→¬(A∨B)
Conclusion : A≡C

____

Premise 1: (A∨B)∨C
Premise 2 : ¬B∧¬C
Conclusion : A

____

Premise : ¬(A ∨ B)
Conclusion : ¬A ∧ ¬B

_____

Premise : ¬A ∧ ¬B
Conclusion : ¬(A ∨ B)
Thank you so much !

What are the rules you are given to prove the above??