How to Approach a Logic Proof Involving Conditionals?

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    Logic Proofs
In summary: U=>~F..........Tautology6. ~F................3,4 Modus Ponens7. ~F=>~P..........Tautology8. ~P................2,6 Modus Ponens9. ~P=>U.............Tautology10. U................8,9 Modus Ponens11. ~U & U..........4,10 Conjunction12. U................11 Contradiction13. ~U=>U............10,12 Proof by Contradiction14. U................13,1 Modus PonensIn summary, to prove U given the premises ~P=>U, P=>F, and F=>
  • #1
averyjedwards2
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hi! I've been studying formal proofs for my logic final and i had a question on this one that i found in my textbook:
1.)~P\supset(horseshoe)U
2.)P\supsetF
3.)F\supsetU\thereforeU

i just have had a little trouble in the past getting started with proofs. Can anyone give me a little push and maybe start me out with this proof? thank you!
 
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  • #2
Re: Formal Proofs Help!

Hi!

First, since you are already using LaTeX commands, I suggest enclosing your formulas in dollar signs. Note, however, that tokens that start with a letter must be separated from a previous command (that start with a backslash) with a space. For example, F should be separates from the preceding \supset, which gives $\supset F$. Otherwise, \supsetF will be considered as one undefined command.

Second, I am not sure what your problems are about: sets, propositional logic or something else. Please describe the context and the notations used, such as ~, $U$ and $F$.
 
  • #3
Re: Formal Proofs Help!

okay thanks for the help! also I'm working on proving this using the 19 rules of inference
 
  • #4
Re: Formal Proofs Help!

averyjedwards2 said:
I'm working on proving this using the 19 rules of inference
This helps, but you have not answered other questions.
 
  • #5
Re: Formal Proofs Help!

averyjedwards2 said:
hi! I've been studying formal proofs for my logic final and i had a question on this one that i found in my textbook:
1.)~P\supset(horseshoe)U
2.)P\supsetF
3.)F\supsetU\thereforeU

i just have had a little trouble in the past getting started with proofs. Can anyone give me a little push and maybe start me out with this proof? thank you!

You mean Given :

1. ~P=>U

2. P=>F

3. F=>U ,then prove U

4. ~U..............ASSUMPTION for contradiction
 

Related to How to Approach a Logic Proof Involving Conditionals?

1. What is a logic proof?

A logic proof is a method used in mathematics and logic to demonstrate the validity of an argument or statement. It involves using a series of logical steps to reach a conclusion based on given premises or assumptions.

2. How do I approach solving a logic proof?

The first step is to read and understand the given premises and the desired conclusion. Then, identify the logical operators (such as "and", "or", "not") and the relationships between the statements. Next, choose a logical strategy (such as direct proof, proof by contradiction, or proof by contraposition) and begin breaking down the argument into smaller steps. It is important to use deductive reasoning and follow the rules of logic throughout the process.

3. What are some common mistakes to avoid when solving logic proofs?

Some common mistakes include assuming information that is not explicitly stated in the premises, using faulty logic, and making incorrect assumptions about the given statements. It is also important to double check each step and make sure they are logically sound before moving on to the next step.

4. Can I use diagrams or illustrations to solve logic proofs?

Yes, diagrams and illustrations can be helpful tools in solving logic proofs. They can help visually represent the relationships between statements and can assist in identifying potential logical fallacies. However, it is important to remember that the proof should ultimately be written out using logical symbols and language.

5. Are there any resources or tips for improving my logic proof solving skills?

Practice is key when it comes to improving logic proof solving skills. It is also helpful to familiarize yourself with the different logical strategies and to seek out additional resources, such as textbooks or online tutorials, to gain a better understanding of the concepts. It can also be beneficial to work through proofs with a study group or seek guidance from a teacher or tutor.

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