CS 251 – Discrete Structures II.
Homework 5
1. Pg 530, Question 1(c,e,f). Use Skolem’s algorithm, to transform each wff into a clausal
form.
1c. x y(p(x,y)q(x)).
1e. xy(p(x,y) z q(x,y,z))
1f. x y z [(p(x,y) q(x,z) r(x,y,z)].
2. Pg 531, Question 4(b, c). Compute the composition of each of the following pairs of
substitutions.
4b. ={x/y}, ={y/x,x/a}
4c. ={x/y, y/a}, ={y/x}
3. Pg 531 Q 5a, 6a. Use Robinson’s unification algorithm and Martelli-Montanari
unification algorithm to find a most general unifier for the following set of atoms.
5a.6a. {p(x, f(y, a), y), p(f(a, b), v, z)}
4. Pg 532. 10a. Prove that the following statement is valid by using resolution to prove
that its negation is unsatisfiable.
10a. x p(x) x p(x).