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.)
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
WEBASSIGN F/EPPS DISCRETE MATHEMATICS
- Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.arrow_forwardGive an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.arrow_forwardProve Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .arrow_forward
- 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.arrow_forwardLabel each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.arrow_forwardLabel each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,