Prove the following argument is valid (and provide reasons):
- ~N v (~B*D)
- ~C --> ~D therefore ~(~C*N)
Our work (so far):
- ~N v (~B*D)
- ~C --> ~D therefore ~(~C*N)
- D-->C (contrapositive of 2)
- ~N v (~B*C) (substitution 3 into 1)
- ~N v ~(B v ~C) (Demorgan's on 4)
- (~N v ~B)*(~N v C) (distribute 4)
- ~(N*B)*(C v ~N) (demorgan's and commutive on 6)
...
- C v ~N
- ~(~C*N) (Demorgan's on the previous statement, which is being numbered 1 again even though I gave it number 99)
Line 7 has C v ~N in it, but I can't show that ~(N*B) is true, or that (~Nv~B) in line 6 is true.
This is where I've been for the past 6 hours. Help me out if you can. Thanks.