Discrete Mathematics

142 DISCRETE MATHEMATIC.,_

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Example

7 Let

A=

{1,

2,

3

},

B = {r, s

}.

Then R = {(1, r), (2,

s)

(3, r)} is the relation from A to B.

Example

8

(1)

A and

Bare

sets

of

real numbers.

We

define the following relation R (equals) from A to B.

aRb

iff

a=

b.

(2) A = { 1, 2, 3, 4, 5} = B

Define the following relation R(less than) on A.

a R b

iff

a < b Then,

R = {(1,

2),

(1, 3), (1,

4),

(1, 5), (2, 3), (2, 4), (2, 5), (3,

4),

(3, 5), (4,

5)}

In this example let R be the relation. Then,

Dom(R)

= {1,

2,

3, 4} and Ran(R) = {2, 3, 4, 5}

If

R is a relation from A to B and x E A we define R(x), the R-relative set

of

x, to be