Example 48 - Chapter 1 Class 12 Relation and Functions
Last updated at Jan. 28, 2020 by Teachoo
Last updated at Jan. 28, 2020 by Teachoo
Transcript
Example 48 Show that the number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two. Total possible pairs = { (1, 1) , (1, 2), (1, 3), (2, 1) , (2, 2), (2, 3), (3, 1) , (3, 2), (3, 3) } Each relation should have (1, 2) and (2, 1) in it For other pairs, Let’s check which pairs will be in relation, and which won’t be Total possible pairs = { (1, 1) , (1, 2), (1, 3), (2, 1) , (2, 2), (2, 3), (3, 1) , (3, 2), (3, 3) } Reflexive means (a, a) should be in relation . So, (1, 1) , (2, 2) , (3, 3) should be in a relation Symmetric means if (a, b) is in relation, then (b, a) should be in relation . So, since (1, 2) is in relation, (2, 1) should also be in relation Transitive means if (a, b) is in relation, & (b, c) is in relation, then (a, c) is in relation So, if (1, 2) is in relation, & (2, 1) is in relation, then (1, 1) should be in relation Relation R1 = { Total possible pairs = { (1, 1) , (1, 2), (1, 3), (2, 1) , (2, 2), (2, 3), (3, 1) , (3, 2), (3, 3) } So, smallest relation is R1 = { (1, 2), (2, 1), (1, 1), (2, 2), (3, 3) } If we add (2, 3), then we have to add (3, 2) also , as it is symmetric but, as (1 , 2) & (2, 3) are there, we need to add (1, 3) also , as it is transitive As we are adding (1, 3), we should add (3, 1) also, as it is symmetric Relation R2 = { Hence, only two possible relations are there which are equivalence (1, 1) , (2, 2) , (3, 3)
Examples
Example 2
Example 3
Example 4 Important
Example 5
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 Deleted for CBSE Board 2021 Exams only
Example 16 Deleted for CBSE Board 2021 Exams only
Example 17 Deleted for CBSE Board 2021 Exams only
Example 18 Important Deleted for CBSE Board 2021 Exams only
Example 19 Important Deleted for CBSE Board 2021 Exams only
Example 20 Deleted for CBSE Board 2021 Exams only
Example 21 Deleted for CBSE Board 2021 Exams only
Example 22 Deleted for CBSE Board 2021 Exams only
Example 23 Important Deleted for CBSE Board 2021 Exams only
Example 24 Deleted for CBSE Board 2021 Exams only
Example 25 Important Deleted for CBSE Board 2021 Exams only
Example 26 Deleted for CBSE Board 2021 Exams only
Example 27 Important Deleted for CBSE Board 2021 Exams only
Example 28 Deleted for CBSE Board 2021 Exams only
Example 29 Deleted for CBSE Board 2021 Exams only
Example 30 Deleted for CBSE Board 2021 Exams only
Example 31 Deleted for CBSE Board 2021 Exams only
Example 32 Deleted for CBSE Board 2021 Exams only
Example 33 Deleted for CBSE Board 2021 Exams only
Example 34 Deleted for CBSE Board 2021 Exams only
Example 35 Deleted for CBSE Board 2021 Exams only
Example 36 Deleted for CBSE Board 2021 Exams only
Example 37 Deleted for CBSE Board 2021 Exams only
Example 38 Deleted for CBSE Board 2021 Exams only
Example 39 Deleted for CBSE Board 2021 Exams only
Example 40 Deleted for CBSE Board 2021 Exams only
Example 41 Important
Example 42 Important
Example 43 Important
Example 44
Example 45 Important Deleted for CBSE Board 2021 Exams only
Example 46 Important
Example 47 Important
Example 48 Important You are here
Example 49
Example 50
Example 51 Important
Examples
About the Author