Question

There are 4096 relations from set A to B.If set A has 6 elements,then how many the number of elements in the set B​

Answer 1

Given :- There are 4096 relations from set A to B.If set A has 6 elements,then how many the number of elements in the set B ?

Solution :-

Let us assume that, there are x elements in set B .

so,

→ A has elements = 6

then,

→ A * B has elements = 6 * x = 6x .

since the number of subsets of an n element set is 2^n .

A/q,

→ 2^(6x) = 4096

→ 2^(6x) = 2^12

since a^m = a^n => m = n

→ 6x = 12

→ x = 2 (Ans.)

Hence, there are 2 elements in set B .

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Answer 2

Given :  There are 4096 relations from set A to B.

set A has 6 elements,

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

Solution:

4096 relations from set A to B.

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

Relation from set A to B = 4096  = 2¹²

Equating Both

=> n(A) * n(B) = 12

n(A) = 6

=> 6 * n(B) = 12

=> n(B) = 2

number of elements in the set B​  = 2

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