CS 281 Solutions to Test II
April 7, 1998

1(a)
(b) .

2 (a)
(b) {(
(c) { }
(d) {(3,1,5), (3,2,5), (7,1, 5), (7,2,5)}

3.
=

4. Let S be the set to be defined.
Basis Clause:
Inductive Clause: If , then .
Extremal Clause: Nothing is in S unless it is obtained from the above two clauses.

5(a) Procedure 2_Mod_3(x):
if x < 2, then return "No"
else if x = 2, then return "Yes"
else return 2_Mod_3(x-3).

(b) T is the set of positive integers congruent to 2 Modulo 3.