1.  (a)  Below is a partially completed table giving A u B,
A n B, A u B, and A n B for various
sets A and B. (Assume that a,b,c,... refer to distinct objects. Note
that I am using n and u as a rough approximation to the union and
intersection symbols due to limitations in web browser technology.
Complete the table. 
 
A 
B 
A u B 
A n B 
A u B 
A n B 
{a,b,c,d,e} 
{b,c,d,e,f} 
{a,b,c,d,e,f} 
{b,c,d,e} 
6 
4 
{a,b} 
{d} 
{a,b,d} 
Ø 
3 
0 
{a,c,e} 
{c,d,e} 




{a,b,f} 
{a,b,c,d,e,f} 




{b,c,d,e} 
{c,f,g} 





 (b) 
Can you give a formula for A u B in terms
of A, B, and A n B? If so, explain why it is true. 

2.  We discussed the power set P(S) of a set S in class. An
example of a power set is
P({black,white}) = { Ø, {black}, {white}, {black,white} }.

 (a)  List the elements of the power set of
{blue,red,yellow}. 
 (b)  What is the size of the power set of
{puce,turquoise,taupe,khaki,lime,cyan,emerald}? (You do not have to list
all the elements of the power
set, just give its size.) 

3.  Write out the mathematical notation used as
shorthand for the following phrases. 
 (a)  x is not a member of the empty set. 
 (b)  The empty set is a subset of the powerset of U. 
 (c)  The intersection of A and B is equal to the union
of C and D. 
 (d)  The complement of X is a superset of Y. 
 (e)  X is the set of ordered pairs in which the first
item in the pair is taken from set Y and the second item is taken
from set Z. 

4.  Let R be the relation between people and the cars
they own; that is, the pair (x,y) is in R if x is a person, y is a car,
and x owns y. Does R represent a function? Why or why not?
