# Example 32 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 32 (Introduction) Let P be the set of all subsets of a given set X. Show that : P P P given by (A, B) A B and : P P P given by (A, B) A B are binary operations on the set P Let X = {1, 2, 3} Subsets of X are , {1}, {2}, {3}, {1, 2}, {1, 3} , {2, 3} , {1, 2, 3} P is a set of all subsets of X. Hence P = { , {1}, {2}, {3}, {1, 2}, {1, 3} , {2, 3} , {1, 2, 3} } If we take union of any 2 elements of P and calculate its union, it will always fall in P For example Taking 2 elements {1} and {1, 2} ( {1}, {1, 2}) {1} {1, 2} {1, 2} This {1, 2} is in P So, is a binary operation Similarly, for intersection( ) ( {1}, {1, 2}) {1} {1, 2} {1} This {1, 2} is in P So, is a binary operation Lets prove it generally Example 32 Let P be the set of all subsets of a given set X. Show that : P P P given by (A, B) A B and : P P P given by (A, B) A B are binary operations on the set P Union : P P P (A, B) A B P is a the set of all subsets of a given set X Here, A & B are in set P, hence we can say that A and B are also subsets of X If we calculate A B A B will be a subset of X as union of subsets is also a subset Hence, A B will also be in set P So, is a binary operation Intersection : P P P (A, B) A B P is a the set of all subsets of a given set X Here, A & B are in set P, hence we can say that A and B are also subsets of X If we calculate A B A B will be a subset of X as union of subsets is also a subset Hence, A B will also be in set P So, is a binary operation

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14

Example 15

Example 16

Example 17

Example 18 Important

Example 19 Important

Example 20

Example 21

Example 22

Example 23 Important

Example 24

Example 25 Important

Example 26

Example 27

Example 28 Important

Example 29

Example 30

Example 31

Example 32 You are here

Example 33

Example 34

Example 35

Example 36

Example 37

Example 38

Example 39

Example 40

Example 41

Example 42 Important

Example 43

Example 44

Example 45 Important

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51

Chapter 1 Class 12 Relation and Functions

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.