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

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8 Important

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

Example 15 Deleted for CBSE Board 2023 Exams

Example 16 Deleted for CBSE Board 2023 Exams

Example 17 Deleted for CBSE Board 2023 Exams

Example 18 Important Deleted for CBSE Board 2023 Exams

Example 19 Important Deleted for CBSE Board 2023 Exams

Example 20 Deleted for CBSE Board 2023 Exams

Example 21 Deleted for CBSE Board 2023 Exams

Example 22 Deleted for CBSE Board 2023 Exams

Example 23 Important Deleted for CBSE Board 2023 Exams

Example 24 Deleted for CBSE Board 2023 Exams

Example 25 Important Deleted for CBSE Board 2023 Exams

Example 26 Deleted for CBSE Board 2023 Exams

Example 27 Important Deleted for CBSE Board 2023 Exams

Example 28 (a) Deleted for CBSE Board 2023 Exams

Example 28 (b)

Example 28 (c)

Example 29 Deleted for CBSE Board 2023 Exams

Example 30 Deleted for CBSE Board 2023 Exams

Example 31 Important Deleted for CBSE Board 2023 Exams

Example 32 Deleted for CBSE Board 2023 Exams

Example 33 Deleted for CBSE Board 2023 Exams

Example 34 Deleted for CBSE Board 2023 Exams

Example 35 Deleted for CBSE Board 2023 Exams

Example 36 Deleted for CBSE Board 2023 Exams

Example 37 Important Deleted for CBSE Board 2023 Exams

Example 38 Deleted for CBSE Board 2023 Exams

Example 39 Deleted for CBSE Board 2023 Exams

Example 40 Deleted for CBSE Board 2023 Exams

Example 41

Example 42 Important You are here

Example 43 Important

Example 44

Example 45 (a) Deleted for CBSE Board 2023 Exams

Example 45 (b) Deleted for CBSE Board 2023 Exams

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51 Important

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at Jan. 28, 2020 by Teachoo

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

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.