(b) Define Equivalence Relation with an example. Give an example of a relation which is not symmetricbut anti-symmetric. Give an example of a relation which is reflexive but not transitive.

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Answered: (b) Define Equivalence Relation with an…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 7CA

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Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Does the relation is less than for a numbers have a reflexive property consider one number? A symmetric property consider two numbers? A transitive property consider three numbers?
Is every relation a function? Is every function a relation?
Does the relation is greater than have a reflexive property consider real number a? A symmetric property consider real numbers a and b? A transitive property consider real numbers a, b and c
Give an example of a relation which is (i) reflexive and transitive but not symmetric; (ii) symmetric and transitive but not reflexive; (iii) reflexive and symmetric but not transitive; (iv) symmetric but neither reflexive nor transitive; (v) transitive but neither reflexive nor symmetric.
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Please explain the steps.
Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (г, у) € {(а, а), (1,1), (а, 1), (1, а), (3, 1), (1,3), (3, а), (а, 3), (ь, b), (b, 2), (2, с)}
Please solve (c) and (d) only, thank you!
Does this digraph illustrate a relation that is symmetric or transitive or neither? symmetrid Enter text [more.] List the ordered pairs that would need to be added to the relation pictured in the digraph in order to make the relation reflexive.
For the relation, indicate whether the relation is:• Reflexive, anti-reflexive, or neither• Symmetric, anti-symmetric, or neither• Transitive or not transitiveJustify your answer.
Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 = %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is, x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.

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(b) Define Equivalence Relation with an example. Give an example of a relation which is not symmetric but anti-symmetric. Give an example of a relation which is reflexive but not transitive.