Kenneth Rosen Edition 7 Exercise 1.6 Question 30 (Page No. 80)

Question

Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is happy.”

Answer 1

Solution:

Let :

• p be the proposition ”Allen is a good boy”,

• q be the proposition ”Hillary is a good girl” and

• r be the proposition ”David is happy”.

Then, our assumption are ¬p ∨ q and p ∨ r.

Steps

1. ¬p ∨ q Premise

2. p ∨ r Premise

3. q ∨ r resolution It is a direct application of resolution rule.