Answer :

i. If A = Φ, find n[P(A)]

A is a set containing some elements.   
P(A) = power set = the set of all subsets of A = power set of A.
As Φ represents 0 elemets.
n(A) = cardinality of A = 0  

n[ P(A) ] = cardinality of P(A)

N[P(A)] = 20 = 1

ii) If n(A) = 3, find n[P(A)]

A is a set containing some elements.   
P(A) = power set = the set of all subsets of A = power set of A.

n(A) = cardinality of A = 3   

n[ P(A) ] = cardinality of P(A)
N[P(A)] = 2n
where n of no of elements

N[P(A)] = 23 = 8


iii) If n[P(A)] = 512 find n(A)
A is a set containing some elements.   
P(A) = power set = the set of all subsets of A = power set of A.

n(A) = cardinality of A    and   

n[ P(A) ] = cardinality of P(A)
N[P(A)] = 2n
where n of no of elements
so  512  =  2n        
so 29 = 2n

n = 9 
so n(A) = 9




iv.
 If n[P(A)] = 1024 find n(A)

A is a set containing some elements.   
P(A) = power set = the set of all subsets of A = power set of A.

n(A) = cardinality of A    and    n[ P(A) ] = cardinality of P(A)

 let  P(A) = n
 then   n[ P(A) ] = 2n  = 1024 = 210
       so  n = n(A) = 10 






Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

i. If A = Φ, Tamilnadu Board Math Term-I

Find the number oTamilnadu Board Math Term-I

Write down the poTamilnadu Board Math Term-I

If n(X) = m, n(Y)Tamilnadu Board Math Term-I

The number of eleTamilnadu Board Math Term-I

Let A and B be twTamilnadu Board Math Term-I

Let

<spTamilnadu Board Math Term-I

If n[P(A)] = 1, wTamilnadu Board Math Term-I

If n(A ∩</sTamilnadu Board Math Term-I