How Do I Apply Natural Deduction to These Logic Problems?

In summary, the conversation is about seeking help with natural deduction problems and the user has provided several premises with corresponding conclusions that they need help proving. They are also reminded to show their progress when posting questions and to limit the number of questions per post.
  • #1
TremblayFil
1
0
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 !
 
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  • #2
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?
 
  • #3
TremblayFil said:
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??
 

FAQ: How Do I Apply Natural Deduction to These Logic Problems?

What is natural deduction?

Natural deduction is a formal system of logic used to construct valid arguments and proofs. It involves using a set of rules and axioms to derive conclusions from given premises.

How is natural deduction different from other types of deduction?

Natural deduction is different from other types of deduction, such as truth tables or Venn diagrams, because it relies on the use of logical rules and principles to construct proofs. It is a more systematic and rigorous approach to reasoning.

What are the basic rules of natural deduction?

The basic rules of natural deduction include the rules of inference, such as modus ponens and modus tollens, as well as the rules of replacement, such as double negation and De Morgan's laws. These rules are used to manipulate propositions and derive new conclusions.

How do I use natural deduction to prove a statement?

To use natural deduction to prove a statement, you must first identify the premises and conclusion of the argument. Then, you can use the rules of natural deduction to manipulate the premises and arrive at the conclusion. This process involves constructing a proof tree, which shows the logical steps taken to reach the conclusion.

What are some common mistakes to avoid when using natural deduction?

Some common mistakes to avoid when using natural deduction include confusing the rules of inference and replacement, forgetting to consider all possible cases, and assuming a conclusion without proper justification. It is important to carefully follow the rules and be thorough in your reasoning to avoid these errors.

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