
Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Example 5, Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a b} is an equivalence relation. R = {(a, b) : 2 divides a b} Check reflexive Since a a = 0 & 2 divides 0 , eg: 0 2 = 0 2 divides a a (a, a) R, R is reflexive. Check symmetric If 2 divides a b , then 2 divides (a b) i.e. b a Hence, If (a, b) R, then (b, a) R R is symmetric Check transitive If 2 divides (a b) , & 2 divides (b c) , So, 2 divides (a b) + (b c) also So, 2 divides (a c) If (a, b) R and (b, c) R, then (a, c) R Therefore, R is transitive. Thus, R is an equivalence relation in Z.
Examples
Example 2
Example 3
Example 4 Important
Example 5 You are here
Example 6 Important
Example 7
Example 8
Example 9
Example 10
Example 11 Important
Example 12 Important
Example 13 Important
Example 14 Important
Example 15 Not in Syllabus - CBSE Exams 2021
Example 16 Not in Syllabus - CBSE Exams 2021
Example 17 Not in Syllabus - CBSE Exams 2021
Example 18 Important Not in Syllabus - CBSE Exams 2021
Example 19 Important Not in Syllabus - CBSE Exams 2021
Example 20 Not in Syllabus - CBSE Exams 2021
Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Not in Syllabus - CBSE Exams 2021
Example 23 Important Not in Syllabus - CBSE Exams 2021
Example 24 Not in Syllabus - CBSE Exams 2021
Example 25 Important Not in Syllabus - CBSE Exams 2021
Example 26 Not in Syllabus - CBSE Exams 2021
Example 27 Important Not in Syllabus - CBSE Exams 2021
Example 28 Not in Syllabus - CBSE Exams 2021
Example 29 Not in Syllabus - CBSE Exams 2021
Example 30 Not in Syllabus - CBSE Exams 2021
Example 31 Not in Syllabus - CBSE Exams 2021
Example 32 Not in Syllabus - CBSE Exams 2021
Example 33 Not in Syllabus - CBSE Exams 2021
Example 34 Not in Syllabus - CBSE Exams 2021
Example 35 Not in Syllabus - CBSE Exams 2021
Example 36 Not in Syllabus - CBSE Exams 2021
Example 37 Not in Syllabus - CBSE Exams 2021
Example 38 Not in Syllabus - CBSE Exams 2021
Example 39 Not in Syllabus - CBSE Exams 2021
Example 40 Not in Syllabus - CBSE Exams 2021
Example 41 Important
Example 42 Important
Example 43 Important
Example 44
Example 45 Important Not in Syllabus - CBSE Exams 2021
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50
Example 51 Important
About the Author