(a) {1,2,3}
(b) {
}.
June 16, 1997
1. Find all the subsets of the following sets:
(a) {1,2,3}
(b) { }.
2. Find the following Cartesian products:
(a) { 
(b) { 
3 (a) If a set A is not a subset of B and 
,
then does 
hold ? Give your reason.
(b) Prove 
.
4 (a) Recursively define the set of odd integers.
(b) Recursively define the set of natural numbers which produce 2 for the remainder
when divided by 3.
5. Prove the following by induction:
(a) 
.
(b) 
if 
for i = 1,2, ..., n.
Logical Equivalences and Implications
