CS151 Class Test 3, 8 December 2005, 13:00
Sample solutions <<Comments to correctors in brackets>>

1.
A x B = {(car, 0), (car, 1), (bicycle, 0), (bicycle, 1), (airplane, 0), (airplane, 1)}

2.
{a, b} x {\emptyset} x {0, 1} = {(c, \emptyset, 0), (c, \emptyset, 1), (b, \emptyset, 0), (b, \emptyset, 1)}

3.
C = {(car, 0), (bicycle, 0), (airplane, 1)} <<or any of the other seven possibilities>>

4.
(5,4) is an element of f
(6,7) is an element of f

<<or any others from the infinite number of possibilies, such as (0, -11), (-1, -14), (1, -8),...>>

5.
f(f(g(f(g(21))))) = 424
g(f(g(g(f(0))))) = 22

6.
b(x) = g(f(f(x)))

<<or anything else that means the same thing such as "b is two compositions of f followed by g" or "b = g after f after f"
or "g(f(f(0)))=44">>