JEE Mathematics/ Lakshmikanta Satapathy/ Set theory part 3/ JEE question on Power set of the cartesian product of two sets solved with the related concepts

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
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