# Messy Logic Problem

1. Jan 10, 2008

### hayden_kee

Hi,

Really struggling with this logic problem, would be very grateful to anyone willing to help

A v D
(~B ^ ~C) <==> D
B ==> ~(C ==> A)
---------------------
~B

Thanks in advance

Hayden Kee

2. Jan 11, 2008

### HallsofIvy

Staff Emeritus
What exactly do you want to do? Determine whether or not the argument is valid?

What happens if you take A true, B true, C false, and D false?

3. Jan 11, 2008

### hayden_kee

trying to derive the conclusion
I did eventually work it out by assuming B and C to be true, after which I was able to show that D must be false, which allowed me to Eliminate the D v A disjunction showing that A is the result either way. Therefore I was left with C==>A which proved that my assumption of B must be false because of the third premise.

Thanks,

Hayden

4. Jan 11, 2008

### Philomancer

I've also assumed B and C, with the C sub-derivation ending with A, and the final three lines of the B sub-derivation ending with the following:
W| C => A
X| B => ~(C =>A)
Y| ~(C =>A)

This allows ~I for the conclusion of ~B through the B assumption (line 4), and the contradictory pair on lines W and Y:

Z| ~B 4, W, Y, ~I

What I can't figure out is how to get A on the C sub-derivation. :S

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