Example 42 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Jan. 28, 2020 by Teachoo

Example 42 - Let (x, y) R (u, v) if and only if xv = yu - Examples

Example 42 - Chapter 1 Class 12 Relation and Functions - Part 2

Example 42 - Chapter 1 Class 12 Relation and Functions - Part 3

Example 42 - Chapter 1 Class 12 Relation and Functions - Part 4

Maths Crash Course - Live lectures + all videos + Real time Doubt solving!

Join Maths Crash Course now

Transcript

Example 42 Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv = yu. Show that R is an equivalence relation. If (x, y) R (u, v) , then xv = yu Check Reflexive If (x, y) R (x, y), then xy = yx Since, xy = yx Hence , R is reflexive. Check symmetric If (x, y) R (u, v) , then xv = yu Now, If (u, v) R (x, y) , then uy = vx Since, xv = yu, vx = uy ∴ uy = vx So, if (x, y) R (u, v) , then (u, v) R (x, y) So, R is symmetric. If (x, y) R (u, v) , then xv = yu If (u, v) R (a, b) , then ub = va u = 𝑣𝑎/𝑏 We need to prove that (x, y) R (a, b) , i.e. xb = ya We need to prove that (x, y) R (a, b) , i.e. xb = ya Check transitive Putting (2) in (1) xv = yu xv = y(𝑣𝑎/𝑏) xvb = yva xb = ya Hence (x, y) R (a, b) So, if (x, y) R (u, v) & (u, v) R (a, b) , then (x, y) R (a, b) Thus R is transitive. Thus, R is an equivalence relation.

Next: Example 43 Important → Ask a doubt (live)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular