Discrete Mathematics for Computer Science

Operations on Functions 243

(b)

p Iq r Fpqr

I 1 1 1

1 1 0 1

1 0 1 0

1 0 0 0

(^0 1 1 0)
0 1 0 1
0 0 1 0
0[0 0 1
(c)

pV qY r F(p,q,r)

1 1 1 0

1 1 0 1

1 0 1 1

1 0 0 0

0 1 1 1

0 1 0 1

0 0 1 1

0 0 0 0

rnOperations on Functions

Since functions and partial functions are special types of binary relations, all operations

defined on binary relations can be applied to functions. The most interesting operations,

however, are composition and inversion.

4.3.1 Composition of Functions

The definition of the composition of functions is exactly the same as that of the composition

of relations. We merely restate it here using the vocabulary of functions.