Question

If A={0,1,2} Find n(P(P(P(P(A)))))

Class-11th
Set

Answer 1

Step-by-step explanation:

Given:-

A={0,1,2}

To find:-

Find n(P(P(P(P(A)))))

Solution:-

Given set is A = {0,1,2}

Number of elements in A = 3

=>n(A)=3

We know that

The number of elements in a set A is n then the total number of subsets to the set are 2^n

Number of subsets of the given set A

=2^3

=>8

The set of all subsets of a set A is called its Power set and it is denoted by P(A)

=>n(P(A))=8

and

Now the set = P(A)=8

Total number of subsets = = 2^8

n(P(P(A))) = 256

Since P(A) has 8 elements.

and

The set =P(P(A)) has 256 elements

Number of subsets = 2^256

n(P(P(P(A))))= 2^256

Now the set = P(P(P(A))

P(P(P(A))) has 2^256 elements

The number of subsets = 2^(2^256)

n(P(P(P(P(A))))) = 2^(2^256)

Answer:-

The value of n(P(P(P(P(A))))) for the given problem is 2^(2^256)

Used formulae:-

• The number of elements in a set A is n then the total number of subsets to the set are 2^n
• The set of all subsets of a set A is called its Power set and it is denoted by P(A)