Help with Logic Proof: Establishing 7.

In summary, to begin establishing 7 in a logic proof, you must first identify the given premises and the conclusion you are trying to prove. It is important to establish 7 because it serves as the foundation for proving the validity of a logical argument. Some common strategies for establishing 7 include using logical rules and principles, truth tables, and logical equivalences. To know if you have successfully established 7, you must use valid logical rules and principles, and you can also use truth tables to test the validity of the argument. Some common mistakes to avoid when establishing 7 include using invalid rules, making assumptions not stated in the premises, and misinterpreting logical connections. It is important to carefully follow the rules of logic and clearly explain
  • #1
agapito
49
0
Consider the following proof from Copi's "Symbolic Logic", p. 109:

1. (∃x) ¬Fx Assumption

2. ¬Fy Assumption

3. (∀x) Fx Assumption

4. Fy 3, UI

5. (∀x) Fx ⇒ Fy 3-4, CP

6. ¬(∀x) Fx 5,2 MT

7. ¬(∀x) Fx 1,2-6, EI

8. (∃x) ¬Fx ⇒ ¬(∀x) Fx 1-7, CP

9. (∀x) Fx ⇒ ¬(∃x) ¬Fx 8, Trans, DN

I cannot understand how 7.- is established, everything else is clear. Can someone explain how 1,2-6, EI results in 7. ?
 
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  • #2
Don't (1), "There exist x such that Fx is not true", and (3), "for all x Fx is true", contradict one another?
 

Related to Help with Logic Proof: Establishing 7.

1. How do I begin establishing 7 in a logic proof?

To begin establishing 7 in a logic proof, you must first identify the premises given in the problem and the conclusion you are trying to prove. Then, you can use logical rules and principles to connect the premises and prove the conclusion.

2. What is the importance of establishing 7 in a logic proof?

Establishing 7 in a logic proof is important because it serves as the foundation for proving the validity of a logical argument. It shows the logical connections between the given premises and the conclusion, ensuring that the argument is sound.

3. What are some common strategies for establishing 7 in a logic proof?

Some common strategies for establishing 7 in a logic proof include using the rules of inference (such as modus ponens, modus tollens, etc.), using truth tables to test the validity of the argument, and using logical equivalences to simplify the argument.

4. How do I know if I have successfully established 7 in a logic proof?

You have successfully established 7 in a logic proof if you have used valid logical rules and principles to connect the premises and prove the conclusion. Additionally, you can use truth tables to test the validity of the argument and ensure that it follows the laws of logic.

5. Are there any common mistakes to avoid when establishing 7 in a logic proof?

Yes, some common mistakes to avoid when establishing 7 in a logic proof include using invalid logical rules or principles, making assumptions not stated in the premises, and misinterpreting the logical connections between the premises and the conclusion. It is important to carefully follow the rules of logic and clearly explain each step in the proof.

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