Is the following statement true or false? If R is any symmetric relation on a set A, then R is symmetric. The statement is true Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order. Therefore, by definition of a symmetric relation, R-1 is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R-1 is not symmetric, and so the statement is false. Then by definition of R, y Rx. Since R is symmetric and y R x, then x R y. Since R is symmetric and x R y, then y R x. Then by definition of R, x R-1 y. Then by definition of R-1, xR y. Then by definition of R1, y R-1 x. Proof: -1 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that x R y. 2. ---Select-- 3. Since R is symmetric and y Rx. then x Ry. 4. ---Select--- 5. Therefore, by definition of a symmetric relation, R1 is symmetric, and so the statement is true. Need Help? Read It

Is the following statement true or false? If R is any symmetric relation on a set A, then R is symmetric. The statement is true Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order. Therefore, by definition of a symmetric relation, R-1 is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R-1 is not symmetric, and so the statement is false. Then by definition of R, y Rx. Since R is symmetric and y R x, then x R y. Since R is symmetric and x R y, then y R x. Then by definition of R, x R-1 y. Then by definition of R-1, xR y. Then by definition of R1, y R-1 x. Proof: -1 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that x R y. 2. ---Select-- 3. Since R is symmetric and y Rx. then x Ry. 4. ---Select--- 5. Therefore, by definition of a symmetric relation, R1 is symmetric, and so the statement is true. Need Help? Read It

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

See similar textbooks

Similar questions

In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
True or False Label each of the following statements as either true or false. 2. Every relation on a nonempty set is as mapping.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
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.
Label each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.
2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .
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.
True or False Label each of the following statements as either true or false. Let be an equivalence relation on a nonempty setand let and be in. If, then.
Label each of the following statements as either true or false. If R is an equivalence relation on a nonempty set A, then any two equivalence classes of R contain the same number of element.