Example 32 - Let P be set of all subsets of a given set X - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples

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    Example 15 Not in Syllabus - CBSE Exams 2021

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    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

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    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

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    Example 31 Not in Syllabus - CBSE Exams 2021

    Example 32 Not in Syllabus - CBSE Exams 2021 You are here

    Example 33 Not in Syllabus - CBSE Exams 2021

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    Example 45 Important Not in Syllabus - CBSE Exams 2021

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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

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Example 4 Important

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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 You are here

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

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Example 45 Important Not in Syllabus - CBSE Exams 2021

Example 46 Important

Example 47 Important

Example 48 Important

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Example 50

Example 51 Important

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.