Discrete Mathematics for Computer Science

Basic Definitions 233

Io

10-

7.5

5

2.5

-3 -2 1 2 3

-5

Figure 4.12 F(x) = x^3.
The function SeatOf2, as shown in Figure 4.13, maps the set of students in the class-
room onto the set of chairs in the classroom if every chair is occupied.

Figure 4.13 SeatOf 2.

The function SeatOf3, as shown in Figure 4.14, is not, onto since one or more chairs
remain unoccupied. In this case, two chairs are unoccupied.

Figure 4.14 SeatOf 3.

The function G(x) = x^2 , as shown in Figure 4.15, is not onto.

y

25-

20-

15

10

5-

0x

-4 -2 2 4

--5

Figure 4.15 G(x) = x^2.