(a)
Whether the relation
(b)
Whether the relation
(c)
Whether the relation
(d)
Whether the relation
(e)
Whether the relation
(f)
Whether the relation
(g)
Whether the relation
(h)
Whether the relation
(i)
Whether the relation
(j)
Whether the relation
(k)
Whether the relation
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Elements Of Modern Algebra
- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.arrow_forwardA relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.arrow_forwardLet 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_forward
- Label 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_forwardIn Exercises , prove the statements concerning the relation on the set of all integers. 18. If and , then .arrow_forwardTrue or False Label each of the following statements as either true or false. 2. Every relation on a nonempty set is as mapping.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,