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Discrete Mathematics With Applicat...
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Discrete Mathematics With Applicat...
Suppose that R is a partial order relation on a set A and that B is a sunset of A. The restriction of R to B is defined as follows:
The restriction of R to B
In other words, two elements of B are related by the restriction of R to B if, and only if, they are related by R. Prose that the restriction of R to B is a partial order relation on B. (In less formal language, this says that a subset of a partially ordered set is partially ordered.)
To prove:
The restriction of
Given information:
The restriction of
Concept used:
A relation is called partial order relation if and only if the relation is reflexive, antisymmetric, and transitive.
Proof:
Consider the set
Let
The restriction of
The objective is to prove that
A relation is called partial order relation if and only if the relation is reflexive, antisymmetric, and transitive,
To prove that
For
This shows that
However,
So,
To prove that
For
And
Chapter 8 Solutions
