Textbook Problem

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

   $=\left\{\left(x,y\right)|x\in B,y\in B,\text{and}\left(x,y\right)\in R\right\}.$

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.)