Discrete Mathematics

138 DISCRETE MATHEMATIC..._

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3.4.4

Partial

vs Total

Orders

A partial order is so called because it is not necessary that ordering exists between every pair

of

elements in

the set. For example, Lshoe and Rshoe have no prescribed ordering between them. In the

"is a subset

of'

partial order, for two sets, it is not necessary that either be a subset

of

the other.

When there is no prescribed order between two elements we say that they are

"incomparable".

Definition a and bare incomparable

if

neither

a~b

nor

b:;5a.

Example 4

For

subsets

of

N, {1, 2, 3} and {2, 3, 4} are incomparable. However, a partial order need not ...