Question

If n[P(A)]=256 find n(A)

Answer 1

Let A be a set

So, we know n(A) is called cardinal number of the set A which is equal to number of elements in set A and

p(A) is called power set of A.

Power set p(A) = set of all subsets of set A
We also know that,

If number of elements in set A = n then, n(A) = n

and Number of subsets of power set = 2^n
So equating values, we get
2^n = 256
2^n = 2^8
so, n = 8
Therefore, Number of elements in set A, n = 8

Answer 2

1

Secondary SchoolMath5 points

If n[P(A)] = 256, find n(A)

Ask for details Follow Report by StarTbia17.06.2018

Answers

Rajpool007 Ambitious

N[P(A)]= 2^n(A)
therefore 
256=2^8=2^n(A)
n(A)= 8

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THANK

mysticd Genius

It is given that n[ P(A) ] = 256

********************************

If number of elements in

Set A = n( A ) = m

Number of elements in power

set of A = n[P(A] then

n[ P(A) ] = 2^m

**************************************

Here ,

2^m = n[ P(A)]

=> 2^m = 256 [ given ]

=> 2^m = 2^8

=> m = 8

[ Since , If a^p = a^q then p = q ]

Therefore ,

m = n( A ) = 8