Mathematics for Computer Science

4.5. Finite Cardinality 111

Exam Problems

Problem 4.29.
LetAbe the set containing the five sets:fag;fb;cg;fb;dg;fa;eg;fe;fg, and let
Bbe the set containing the three sets: fa;bg;fb;c;dg;fe;fg. LetRbe the “is
subset of” binary relation fromAtoBdefined by the rule:

X R Y IFF XY:

(a)Fill in the arrows so the following figure describes the graph of the relation,
R:

A arrows B

fag

fa;bg

fb;cg

fb;c;dg

fb;dg

fe;fg

fa;eg

fe;fg

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

function total injective surjective bijective

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

function total injective surjective bijective