a. If ? is a relation defined from the Set ? = { 6,12,25,36} to the set ? = {3,4,5,6} as follows: ? = {(?, ?) ∈ ? × ? | ? ??????? ?} Find the following: i. Relation set of ? in roster form. ii. Domain and Range of the relation R.  iii. Restriction of R on ?, where ? = {6,12}.

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...
icon
Related questions
Question

a. If ? is a relation defined from the Set ? = { 6,12,25,36} to the set ? = {3,4,5,6} as follows:
? = {(?, ?) ∈ ? × ? | ? ??????? ?}
Find the following:
i. Relation set of ? in roster form.
ii. Domain and Range of the relation R. 
iii. Restriction of R on ?, where ? = {6,12}. 
iv. Find the element related to ?, Where ? = {25,36}. 
v. Find the matrix form of R. 
b. Let us consider the sets ? = {2,3,4,5} and ? = { 0,1,2,3}. Define the relation ?: ? → ? such that (? ? ?) if
and only if (? + 5?) is an even number. Verify the statement that ? is an equivalence relation

Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Relations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,