Question

a, b, c be three sets such that n(a)=2, n(b)=3, n(c)=4. if p(x) denotes power set of x. then k=n(p(p(c)))/n(p(p(a)))*n(p(p(b))). sum of digits of k is

Answer 1

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Answer 2

Concept:

The mathematical concept of well-defined groupings of objects, or sets, that are referred to as members or elements of the set. The only sets that are taken into consideration are those whose members are also sets because pure set theory only deals with sets. Formally, arithmetic and the theory of hereditarily-finite sets. Those finite sets whose elements are also finite sets, whose elements are also finite sets, and so on are identical.

Given:

n(a)=2

n(b)=3

n(c)=4

Find:

Sum of digits of k from the given sets.

Solution:

P(A) = 2^2 = 4

P((A)) = 2^4

P(B) = 2^3 = 8

P((B)) = 2^8

P(C) = 2^4 = 16

P((C)) = 2^16

So, from the given question we have:

K = n(P(P(C)))/n(P(P(A))) x n(P(P(B)))

By substituting the values in the given sets.

K = 2^16/2^4 x 2^8

K = 2^16/2^(4 + 8)

K = 2^16/2^12

K = 2^(16 - 12)

K = 2^4

K = 16

Now, we will find the sum of digits which we get from K = 16

Sum of digits = (1 + 6) = 7.

Hence, the sum of digits of K is 7.

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