Introduction to Logic

Exercise 5.2 - Resolution Principle

In each of the following questions, say which of the answers best characterizes the result of applying resolution to the clauses shown.

1.{p, q, ¬r} and {r, s} 
  {p, q, s} 
  {p, q, r, s} 
  {p, q, ¬r, s} 
  There are no resolvents. 
 
2.{p, q, r} and {r, ¬s, ¬t} 
  {p, q, r, ¬s, ¬t} 
  {p, q, ¬s, ¬t} 
  There are no resolvents. 
 
3.{q, ¬q} and {q, ¬q} 
  {q, ¬q} 
  {q} 
  {¬q} 
  {} 
  There are no resolvents. 
 
4.p, q, r} and {p, ¬q, ¬r} 
  {¬p, q, r, p, ¬q, ¬r}
  {q, r, ¬q, ¬r}, {¬p, r, p, ¬r}, {¬p, q, p, ¬q} 
  {p, ¬p}, {q, ¬q}, {r, ¬r} 
  {} 
  There are no resolvents.