Can Modus Ponens and Substitution Solve This Complex Logic Problem?

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In summary, using only modus ponens or substitution, we can prove the statement q -> r -> [ [ p -> q ] -> [ p -> r ] ] by using the three axioms: 1) p -> [ q -> p ], 2) s -> [ p-> q ] -> [ [s -> p] -> [ s -> q ] ], and 3) p -> f -> f -> p where f is "false". By substituting p for f in axiom 3, we can conclude that f -> (p -> f), which can then be used in conjunction with axiom 1 to prove p -> f. Finally, by making the substitutions s ≡ p, p ≡ q, and q
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JustNick
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Using only modus ponens or substitution. Prove:
q -> r -> [ [ p -> q ] -> [ p -> r ] ]

using the three axioms:
1) p -> [ q -> p ]
2) s -> [ p-> q ] -> [ [s -> p] -> [ s -> q ] ]
3) p -> f -> f -> p

where the symbol f is "false."

I am having the hardest time trying to solve this proof, any point in the right direction is appreciated.
 
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If p then it follows from 2). (s≡p ; p≡q ; q≡r) But isn't 3) just p? I guess my understanding of 3) is f.
May I conclude f → (p → f) by 1) and then f → p by 3)? If so I'm done by 2) and the substitutions mentioned.
 
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Related to Can Modus Ponens and Substitution Solve This Complex Logic Problem?

1. What is a challenging logic problem?

A challenging logic problem is a type of puzzle or brain teaser that requires critical thinking and problem-solving skills to come up with a solution. It often involves a set of clues or conditions that must be analyzed and logically deduced to reach a correct answer.

2. How do you solve a challenging logic problem?

To solve a challenging logic problem, you first need to carefully read and understand all of the given clues or conditions. Then, you can use deductive reasoning and trial and error to eliminate possibilities and narrow down the correct answer. It may also be helpful to make a chart or diagram to organize the information.

3. What skills are needed to be good at solving challenging logic problems?

To be good at solving challenging logic problems, you need to have strong critical thinking skills and be able to think logically and analytically. You also need to be patient and persistent, as these problems can sometimes be difficult and require multiple attempts to solve.

4. Are there any strategies that can help with solving challenging logic problems?

Yes, there are several strategies that can be helpful when solving challenging logic problems. These include breaking down the problem into smaller parts, making a chart or diagram to organize information, and using trial and error to test different possibilities. It may also be helpful to work backwards from the given solution to determine the steps needed to reach it.

5. Why are challenging logic problems important in the field of science?

Challenging logic problems are important in the field of science because they help develop critical thinking skills and promote problem-solving abilities. Scientists often encounter complex problems that require them to think outside the box and come up with innovative solutions, and practicing with challenging logic problems can help hone these skills.

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