- #1
TinyTex
- 7
- 0
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
Last edited: