Is This Natural Deduction Problem Solvable?

[TinyTex]

Homework Statement

Prove by natural deduction
((X $\Rightarrow$ ¬Y)$\vee$(¬X$\Rightarrow$Y))$\Rightarrow$(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))

Homework Equations

The Attempt at a Solution

i understand basic natural deduction and how to prove via it but this one has me stumped as there is no $\models$ symbol which normally means that everything to the right is what you have to end up with using everything to the left of the $\models$ symbol

Could really use some help here!

 

[Mark44]

Homework Statement

Prove by natural deduction
((X $\Rightarrow$ ¬Y)$\vee$(¬X$\Rightarrow$Y))$\Rightarrow$(¬(X$\wedge$Y)$\wedge$¬(¬X$\wedge$¬Y))

Homework Equations

The Attempt at a Solution

i understand basic natural deduction and how to prove via it but this one has me stumped as there is no $\models$ symbol which normally means that everything to the right is what you have to end up with using everything to the left of the $\models$ symbol

Could really use some help here!

Is this the same problem you posted in the other thread?

Occasionally someone will post a symbolic logic problem such as this, but as I recall, not many of the members here normally weigh in. Most of us here are better versed in mathematical logic, which uses different symbols, and is usually less theoretic and more applied.

I don't suppose you could use a truth table? The expression on the left of the outer implication is a tautology; i.e., always true. Also, (X $\Rightarrow$ ¬Y) $\Leftrightarrow$ ¬(X$\wedge$Y). Similarly, (¬X $\Rightarrow$ Y) $\Leftrightarrow$ ¬(¬X$\wedge$¬Y). Hope this helps.

 

[TinyTex]

yeah its the same as in the other thread but i managed to work out the resolution bit of it and it would not let me edit the post which looked rather cluttered