(a) {1,3}
(b) {
}. [5 each]
March 26, 1998
1. Find all the subsets of the following sets:
(a) {1,3}
(b) { }. [5 each]
2. Find the following Cartesian products:
(a) 
(b) { 
(c) { 
(d) { 
[5 each]
3 Prove that 
. [20]
4 Recursively define the set of numbers 
given by 
for all positive integers n. [20]
5(a) Write a recursive procedure to test a number to see whether or not it is in the set T recursively defined as follows:
Basis Clause: 
Inductive Clause: If 
, then 
.
Extremal Clause: Nothing is in T unless it is obtained from the basis and inductive clauses. [20]
(b) Describe the set T non-recursively, in English. [10]
Logical Equivalences and Implications - you may use them.
