CS2022/MA2201
HW#1

Due: Tuesday, September 2

1. (6 points) Do Exercise 1.1.8, that is, Exercise 8 on page 11 in Section 1.1 

2. (4 points) Construct truth tables for each of the following compound propositions.
  a) 
  b) 

3. (9 points) a) Prove or give a counterexample to “the transitivity of implication”, 
 .
That is, is the above compound proposition a tautology?
b) Prove or give a counterexample to “the transitivity of conjunction”, that is,
  .
c) Prove or give a counterexample to “the transitivity of exclusive-or”, that is, 
 .

4. (2 points) Do Exercise 1.2.16.

5. (10 points) Do Exercise 1.3.10. Do not use the definition of the cardinality of a set. As a hint, to show that exactly two people satisfy a predicate P you can show that at least two people satisfy P and at most two people satisfy P. 

CS2022/MA2201
HW#1 Solutions

1. a) 
b) 
c) 
d) 
e) 
f)  although  would be acceptable

2. a)
 
b) 

3. a)  is a tautology because

b)  is a tautology because

c)  is not a tautology as seen by the case where p and r are T and q is F, or the case where p and r are F and q is T.

4. 

5. a) 
b) 
c) 
d) 
e) 
f) 
g) 
h) 
i) 
j)