Mathematics for Computer Science

4.4. Binary Relations 83

A arrows C

M

MAND.P IMPLIESM/

PANDQ

Q

PORQ

PORQ

NOT.PANDQ/

PXORQ

(b)Circle the properties below possessed by the relationI:

FUNCTION TOTAL INJECTIVE SURJECTIVE BIJECTIVE

(c)Circle the properties below possessed by the relationI^1 :

FUNCTION TOTAL INJECTIVE SURJECTIVE BIJECTIVE

Homework Problems

Problem 4.12.
Letf WA!BandgWB!Cbe functions andhWA!Cbe their composition,
namely,h.a/WWDg.f.a//for alla 2 A.
(a)Prove that iffandgare surjections, then so ish.

(b)Prove that iffandgare bijections, then so ish.

(c)Iff is a bijection, then so isf^1.