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Three sets have p,q and r elements , the total no. Of non-empty proper subsets of the first set is 120 more than the total no. Of non-empty proper subsets of the second set . The total no of subsets of the third set is 24 more than the second set .The value of p+q+r is

Three sets have p,q and r elements , the total no. Of non-empty proper subsets of the first set is 120 more than the total no. Of non-empty proper subsets of the second set . The total no of subsets of the third set is 24 more than the second set .The value of p+q+r is
 

Grade:11

2 Answers

Arun
25758 Points
2 years ago
Dear student
 
2^p - 1 = 120 + 2^q -1
 
2^p = 120 + 2^q
 
Hence p = 7, q = 3
 
Now
2^r -1 = 24 + 2^q -1
 
2^r = 24 + 2^q
As q = 3
 
2^r = 32
Hence r = 5
 
Hence p +q +r = 7 + 3 + 5 = 15
Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
Dear student

Nom empty proper subset for n elements of set are 2^n -2

Now form the algebraic expression using the given condition and obtain the required answer

Regards

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