Question

If there are 512 relations from a set A={1,2,3} to a set B. then the number
of elements in B is
a)3
b)2
c)4
d)8​

Answer 1

Answer:

a) 3

Step-by-step explanation:

We know that no. of relations from A to B are no. of subsets of (A x B).

No. Of elements in (A x B) = n(A x B) = n(A) * n(B)

Therefore no. Of subsets of (A x B) = 2^n(A)*n(B)

512 = 2^3*n(B)

2^9 = 2^3*n(B)

9=3*n(B)

n(B) = 3

Answer 2

Given,

A = {1,2,3}

There are 512 relations from a set A={1,2,3} to a set B

To Find,

The number of elements in B is =?

Solution,

As the relation from A to B is given by subset of (A x B).

The number of element in (A x B) = n(A)*n(B)

$512 = 2^3*n(B)2^9 = 2^3*n(B)9=3*n(B)n(B) = 3$

Hence, the number of elements in B is 3. Option(a) is the correct answer.