Suppose that R is a partial order relation on a set A and that B is a subset of A. The
Chapter 8, Problem 34(choose chapter or problem)
Suppose that R is a partial order relation on a set A and that B is a subset of A. The restriction of R to B is defined as follows:
The restriction of R to B
= {(x, y) | x \(\in\) B, y \(\in\) B, and (x, y) \(\in\) R}.
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. Prove 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.)
Text Transcription:
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