CSCE 235
Homework
Assignment 2
Assigned: January 21, 2009
Due: 12:30 p.m. January 28,
2009
(Homework 5
minutes late will not be accepted)
1. (25 points) Using only the following logical equivalences: double negation, commutative laws, associative laws, distributive laws, idempotent laws, identity laws, negation laws, De Morgan laws, implication, and equivalence, and the following logical implications: addition, and simplification to logically prove the following, an. You can also use “conjunction”. You must show and explain all steps clearly.
(a) (5 points) exportation law: 
(b) (5
points) modus ponens: 
(c) (5
points) modus tollens: 
(d) (5
points) disjunctive syllogism: 
(e) (5
points)
2. (50 points) Give a formal proof for each of the following using only the rules given in the tables of Logical Equivalences and Implications in your handout 4.
(a) (10 points) If 
, 
, 
, then 
.
(b)
(10 points) If 
and 
, then 
.
(c)
(10 points) If 
, 
, 
, 
, then 
.
(d)
(10 points) If 
, 
, 
, then 
.
(e) (10 points) If 
, , 
, then 
.
3. (20 points) Use
formal proof to prove the following. Use only proof by contradiction.
(a)
(10 points) If , , , then .
(b) (10 points) If and , then .
4. (20 points) (Based on Ross and Wright 1988). Consider the following hypotheses:
If
symptom A or symptom B is observed, then test C is performed. If test D is performed, then test C will not
be performed and whether the patient has illness E will be known. Test C is not performed.
Which of the following conclusions must follow, i.e., can be inferred from the above hypotheses? Justify your answers. (Use a logical proof to prove that a conclusion follows; and may use a line of a truth table to prove that a conclusion does not follow.)
(a) Test D is performed.
(b) Whether the patient has illness E will be known
(c) Symptom B is not observed.
(d) If whether the patient has illness E is known, then test D was performed.
(e) If symptom A is observed, then whether the patient has illness E will not be known.