Prove by both Natural Deduction and Resolution

In summary, the conversation discusses proving a statement using both natural deduction and resolution. The statement is ((X \Rightarrow ¬Y)\vee(¬X\RightarrowY))\Rightarrow(¬(X\wedgeY)\wedge¬(¬X\wedge¬Y)) and the attempt at a solution includes breaking it down into CNF and using various logical operations to simplify it. However, the person is unsure of how to proceed with the resolution method.
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TinyTex
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Homework Statement


Prove by both natural deduction and by resolution
((X [itex]\Rightarrow[/itex] ¬Y)[itex]\vee[/itex](¬X[itex]\Rightarrow[/itex]Y))[itex]\Rightarrow[/itex](¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))

Homework Equations


The Attempt at a Solution


as far as natural deduction on this goes i have no idea since there is no ' I- ' looking symbol so I am clueless

i also got a bit stuck on the resolution this is what i have so far

¬CNF
¬(((X [itex]\Rightarrow[/itex] ¬Y)[itex]\vee[/itex](¬X[itex]\Rightarrow[/itex]Y))[itex]\Rightarrow[/itex](¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y)))

- ((X [itex]\Rightarrow[/itex] ¬Y)[itex]\vee[/itex](¬X[itex]\Rightarrow[/itex]Y))[itex]\wedge[/itex](¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬(X[itex]\wedge[/itex]Y)[itex]\wedge[/itex]¬(¬X[itex]\wedge[/itex]¬Y))
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬((¬X[itex]\vee[/itex]¬Y)[itex]\wedge[/itex](X[itex]\vee[/itex]Y))
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex]¬(¬X[itex]\vee[/itex]¬Y)[itex]\vee[/itex]¬(X[itex]\vee[/itex]Y)
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex](X[itex]\wedge[/itex]Y)[itex]\vee[/itex]¬(X[itex]\vee[/itex]Y)
- ((¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y))[itex]\wedge[/itex](X[itex]\wedge[/itex]Y)[itex]\vee[/itex](¬X[itex]\wedge[/itex]¬Y)

then i don't know what do as it gets stuck i probably did something wrong somewhere i can see that i screwed up my latez on the left hand side i know its (¬X v ¬Y v X v Y) not (¬X [itex]\wedge[/itex] ¬Y)[itex]\vee[/itex](X[itex]\wedge[/itex]Y) its the right hand side which i got stuck on
 
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Related to Prove by both Natural Deduction and Resolution

1. What is "Prove by both Natural Deduction and Resolution"?

"Prove by both Natural Deduction and Resolution" is a method used in logic and mathematics to prove the validity of a statement or argument. It involves using both natural deduction, which is a systematic way of deriving conclusions from premises, and resolution, which is a method of logical inference that involves reducing a statement to simpler forms.

2. What is the difference between Natural Deduction and Resolution?

The main difference between Natural Deduction and Resolution is their approach to proving the validity of a statement. Natural deduction uses a set of predetermined rules and logical steps to derive conclusions, while resolution involves reducing a statement to simpler forms and using resolution rules to determine its validity.

3. How does "Prove by both Natural Deduction and Resolution" work?

First, the statement or argument is broken down into simpler forms using natural deduction. Then, resolution is used to further reduce the statement and determine its validity. If both methods lead to the same conclusion, then the statement is considered to be proven by both natural deduction and resolution.

4. What are the benefits of using "Prove by both Natural Deduction and Resolution"?

Using both natural deduction and resolution allows for a more comprehensive and rigorous approach to proving the validity of a statement or argument. It also helps to identify any potential errors or contradictions in the reasoning process.

5. In what fields is "Prove by both Natural Deduction and Resolution" commonly used?

"Prove by both Natural Deduction and Resolution" is commonly used in fields such as mathematics, logic, computer science, and philosophy. It is also a fundamental concept in artificial intelligence and automated reasoning systems.

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