Question

Let a be a set with cardinality n. there are 512 total number of relations possible on



a. then the value of n is

Answer 1

HELLO DEAR,    

We know:-

 If Set A has cardinality n

then it's    total number of relations are 2^(n²)    

NOW,  

Total number of relations possible = 512  

so,  

2^(n²) = 512  

2^(n²) = 2⁹  

n² = 9  

n² = 3²  

n = 3  

Therefore , n = 3  

 I HOPE ITS HELP YOU DEAR,

 THANKS  

Answer 2

Hi ,

 ********************************

The total number of

relations  that can be

defined from setA   to a

set A ,  

If n( A ) = n

 Total number of relations

= 2^n²

**********************************Here ,  

2^n² = 512

 => 2^n² = 2^9  

=> n² = 9  

[ Since , If a^m = a^n then m = n ]

 n² = 3²  

Therefore ,

 n = 3

 I hope this helps you.

 : )