# Homework Help: Prove by both Natural Deduction and Resolution

1. Jul 18, 2011

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1. The problem statement, all variables and given/known data
Prove by both natural deduction and by resolution
((X $\Rightarrow$ ¬Y)$\vee$(¬X$\Rightarrow$Y))$\Rightarrow$(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))

2. Relevant equations

3. 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 im clueless

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

¬CNF
¬(((X $\Rightarrow$ ¬Y)$\vee$(¬X$\Rightarrow$Y))$\Rightarrow$(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y)))

- ((X $\Rightarrow$ ¬Y)$\vee$(¬X$\Rightarrow$Y))$\wedge$(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$¬(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$¬(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$¬((¬X$\vee$¬Y)$\wedge$(X$\vee$Y))
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$¬(¬X$\vee$¬Y)$\vee$¬(X$\vee$Y)
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$(X$\wedge$Y)$\vee$¬(X$\vee$Y)
- ((¬X $\wedge$ ¬Y)$\vee$(X$\wedge$Y))$\wedge$(X$\wedge$Y)$\vee$(¬X$\wedge$¬Y)

then i dont 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 $\wedge$ ¬Y)$\vee$(X$\wedge$Y) its the right hand side which i got stuck on

Last edited: Jul 18, 2011
2. Jul 19, 2011

*bump