Question

If there are 512 relations from a set A= (2,3,5) to set B , then the number of elements in B is ​

Answer 1

Step-by-step explanation:

No. of relations from A to B = no. of subsets of (A x B).

No. of elements in (A x B) = n(A x B)

Therefore

• No. Of subsets of (A x B) = 2^n(A)*n(B)

512 = 2³*n(B)

2⁹ = 2(³*n(B))

9 = 3*n(B)

n(B) = 3

Answer 2

Given : There are 512  relations from set A to B.

set A = { 2 , 3 , 5}

To Find :  how many the number of elements in the set B​

Solution:

512 relations from set A to B.

set A = { 2 , 3 , 5}

n(A) = 3

Relation from set A to B.  =  $2^{n(A).n(B)}$

Relation from set A to B = 512  = 2⁹

Equating Both

=> n(A) * n(B) =9

n(A) = 3

=> 3 * n(B) = 9

=> n(B) = 3

number of elements in the set B​  = 3

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