Mathematical Foundation of Computer Science

DHARM

DISCRETE THEORY, RELATIONS AND FUNCTIONS 9

y 1 y 2

x 1 11

x 2 01

x 3 10

(a)(b)

(Tabular representation of relation R) (Graph of relation R)

where cell entries 1’s (0’s) stands for where arrows shows the couple

presence (absence) of the ordered couple ordering in the relation.

in the relation.

Fig 1.1

TCS SAIL HCL OIL WIPRO INFOSYS

MCA 01 110101

MCA11 011010

MCA17 010101

MCA28 001001

MCA42 001000

Fig. 1.2 Tabular representation of relation R 1.
Fig. 1.3 shows another binary relation R 2 from X to Y that describes the jobs offer by the
companies to the students.
TCS SAIL HCL OIL WIPRO INFOSYS
MCA 01 110000
MCA11 001010
MCA17 010101
MCA28 001000
MCA42 000000

Fig. 1.3 Tabular representation of relation R 2.

Domain Set and Range Set of Binary Relation

Let R be a binary relation, then domain set (domain) of relation R denoted by D(R), contains all
first components of the ordered couples i.e.
D(R) = {x/(x, y) ∈ R}
Further, if R = X × Y then D(R) ⊆ X.

x 1

x 2

x 3

y 1

y 2