Need Help In Logic / Natural Deduction

In summary, the conversation includes a request for help understanding a new concept in a class involving shorter versions of tables. The speaker provides two examples and asks for confirmation on their solutions, which turn out to be correct and use the DS and HS rules. The conversation ends with a message of encouragement.
  • #1
kj_67
1
0
Hi,

I need help please! :cry:

In the class that I am in we went from doing tables to this shorter version, and I don't get it.

Example:

1. ~JvP
2. ~J
3. S>J /?
4. ?

Would number 4. be ~P>J and the supporting lines be 1,3 with the DS (disjunctive syllogism)? I don't get it...

Would it be the DS rule (pvq/~p//q)?

Another one I don't get:

1. H>D
2. F>T
3. F>H /?
4. ?


Would number 4 be D>F and the conculsion be HS (hypothetical syllogism, p>q/q>r//p>r)?

Thanks...
 
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  • #2
Yes, your answers to both of those examples are correct. The first one uses the DS rule (pvq/~p//q) and the second one uses the HS rule (p>q/q>r//p>r). For the first example, you can think of it as ~JvP being the premise, which implies ~J (1. and 2.). Then S>J is the second premise (3.), so we can use DS to conclude ~P>J (4.). For the second example, F>T is the first premise (2.), followed by F>H (3.). The conclusion then follows from HS, so D>F (4.). I hope this helped. Good luck!
 
  • #3


Hi there,

I understand that you are struggling with natural deduction and logic. It can be a challenging topic, but with some practice and guidance, I am sure you will be able to understand it better. Let me try to explain the examples you provided.

In the first example, you are given three premises: ~JvP, ~J, and S>J. The goal is to use these premises to reach a conclusion. To do this, we use the rules of natural deduction. The first step is to identify the main operator in each premise. In this case, we have the negation (~) and disjunction (v). The main operator in the conclusion should also be a negation, so we want to get rid of the disjunction. To do this, we use the disjunctive syllogism rule (pvq/~p//q). This rule says that if we have a disjunction (pvq) and we know that one of the disjuncts is false (~p), then we can infer the other disjunct (q). In this case, the disjunction is ~JvP, and we know ~J is true (line 2), so we can infer P. This gives us the new line: 4. P.

Next, we need to use the conditional statement (S>J) to reach our conclusion. The conditional statement says that if the antecedent (S) is true, then the consequent (J) must also be true. In this case, we know that S>J is true, and we have already established that P is true. Therefore, we can conclude that J is also true. This gives us the final line: 5. J.

So, the conclusion is J, and the supporting lines are 1, 3, and 4 (for the disjunctive syllogism). The final proof would look like this:

1. ~JvP
2. ~J
3. S>J /?
4. P (DS 1, 2)
5. J (conditional statement 3, 4)

In the second example, you are given three premises: H>D, F>T, and F>H. Again, the goal is to reach a conclusion using these premises. The main operators in these premises are the conditional (>) and the conjunction (&). To reach the conclusion, we need to use the hypothetical syllogism
 

What is logic?

Logic is the study of reasoning and argumentation. It involves understanding how to form and evaluate arguments, as well as how to use rules and principles to determine the validity of claims.

What is natural deduction?

Natural deduction is a logical system that uses rules of inference to demonstrate the validity of arguments. It involves breaking down complex arguments into simpler components and using these rules to show the logical relationships between them.

How can I improve my skills in logic and natural deduction?

To improve your skills in logic and natural deduction, it is important to practice regularly and familiarize yourself with different types of arguments and logical structures. You can also seek out resources such as textbooks, online tutorials, or workshops to learn more about the principles and techniques of logical reasoning.

What are some common mistakes in natural deduction?

One common mistake in natural deduction is confusing the order of premises and conclusions, which can lead to an incorrect argument. Another mistake is using incorrect rules of inference or not following the correct structure of a proof. It is important to carefully check each step and ensure that all rules are being applied correctly.

How is natural deduction used in real life?

Natural deduction is used in many real-life situations, such as in law, mathematics, and computer science. It allows us to evaluate arguments and determine whether they are valid or not, which is crucial in making sound and logical decisions. It also helps us to critically analyze and construct arguments, which is important in fields such as philosophy and debate.

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