Kenneth Rosen Edition 7 Exercise 1.6 Question 31 (Page No. 80)

Question

Use resolution to show that the hypotheses “It is not raining or Yvette has her umbrella,” “Yvette does not have her umbrella or she does not get wet,” and “It is raining or Yvette does not get wet” imply that “Yvette does not get wet.”

Answer 1

define the following proposition as

r: it is raining.

u:Yvette has her umbrella.

w:Yvette get wet.

so from first statement we will get c1 as ~r v u

from second statement  c2 as ~u v ~w.

from third statement c3 as r v ~w

c4: from c1 and c2 - ~r v ~w

from c3 and c4 - ~w v ~w which is equal to ~w and that is conclusion Yvette does not get wet.