Set Theory QA 3
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The document discusses a problem involving two sets, A and B, with 4 and 2 elements, respectively, and calculates the number of subsets of the Cartesian product A × B that contain at least 3 elements. It details the method to determine the total number of subsets and subtracts those with at most 2 elements to arrive at the answer of 219. For further information, it mentions resources and social media links for a physics helpline.
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![Physics Helpline
L K Satapathy
Set Theory 3
Correct option = (a)
Number of Subsets having 0 element 8
0 1C
Number of Subsets having 1 element 8
1 8C
Number of Subsets having 2 elements 8
2
8.7 28
1.2
C
Number of Subsets having at least 3 elements = 256 – 37 = 219 [Ans]
Number of Subsets having at most 2 elements = 1+ 8 + 28 = 37](https://image.slidesharecdn.com/settheory3-160912063258/85/Set-Theory-QA-3-3-320.jpg)
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Set Theory QA 3
- 1. Physics Helpline L K Satapathy Set Theory 3
- 2. Physics Helpline L K Satapathy Set Theory 3 Question : Let A and B be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set A B having at least 3 elements is Answer : ( ) 219 ( ) 256 ( ) 275 ( ) 510a b c d Total number of subsets of (A B) 8 2 256 Given : n(A) = 4 & n(B) = 2 n(A B) = n(A) n(B) = 8 We need to find the number of subsets having at least 3 elements Method : Number of subsets having at least 3 elements = (Total number of subsets) – (number of subsets having at most 2 elements)
- 3. Physics Helpline L K Satapathy Set Theory 3 Correct option = (a) Number of Subsets having 0 element 8 0 1C Number of Subsets having 1 element 8 1 8C Number of Subsets having 2 elements 8 2 8.7 28 1.2 C Number of Subsets having at least 3 elements = 256 – 37 = 219 [Ans] Number of Subsets having at most 2 elements = 1+ 8 + 28 = 37
- 4. Physics Helpline L K Satapathy For More details: www.physics-helpline.com Subscribe our channel: youtube.com/physics-helpline Follow us on Facebook and Twitter: facebook.com/physics-helpline twitter.com/physics-helpline