## Objectives

Express problems using predicate calculus and propositional logic

Use inference for sound reasoning over premises in propositional logic and predicate calculus to conclude properties

Proof by contradiction in Datalog using resolution

## Problems

For the International version of the book, change “Section 1.6” to “Section 1.5”.

Please format your answers as closely to these examples: https://wiki.cs.byu.edu/_media/cs-236/homework_6_examples.pdf

For each of the problems (except Section 1.6 question 24), **you will need to provide a proof** in addition to what the question is asking (unless the conclusion you are asked to prove is incorrect; instead you will need to explain why it is incorrect).

For the problems involving Section 1.6 question 10, you don't need to explain what rules of inference are used as long as you provide a proof.

(6 points) Section 1.6 Problem 6

(2 points) Section 1.6 Problem 8

(6 points) Section 1.6 Problem 10 part a

(8 points) Section 1.6 Problem 10 part b (use resolution)

(3 points) Section 1.6 Problem 16 part b

(3 points) Section 1.6 Problem 16 part d

(2 points) Section 1.6 Problem 24

(4 points) Section 1.6 Problem 34 part a (use resolution)

(6 points) Use resolution to answer the query in **a.dl** below

(6 points) Use resolution to answer the query in **b.dl** below

(6 points) Use resolution to answer the query in **c.dl** below

### a.dl

Schemes:
C(X)
P(X)
W(X)
Facts:
C('d')
Rules:
P(X) :- C(X).
W(X) :- P(X).
Queries:
W(X)?

### b.dl

Schemes:
J(X)
C(X)
P(X)
R(X)
Facts:
J('d')
C('d')
Rules:
P(X) :- J(X).
R(X) :- C(X), P(X).
Queries:
R(X)?

### c.dl

Schemes:
P(X,Y)
Q(X,Y,Z)
R(X,Z)
Facts:
P('a','a')
P('a','b')
P('a','c')
Q('a','b','c')
Rules:
R(X,Z) :- P(X,Z), Q(X,Y,Z)
Queries:
R('a',X)?

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