Question

If there are 1024 relation from a set A={1, 2, 3, 4, 5} to a set B,then the number of element in B is

Answer 1

Answer:

n(B) = 2

Step-by-step explanation:

We know no. of relations from A to B = no. of subsets of (A x B) = 2^n(A x B)

Now n(A x B) = n(A) * n(B)

n(A x B) = 5* n(B)

Therefore, 1024 = 2^5* n(B)

2^10 = 2^5* n(B)

10 = 5* n(B)

n(B) = 2

Hope you understand.

Answer 2

Find the number of elements in set B for the given number of relations.

Explanation:

• Let there be two sets X and Y having elements m and n respectively. $->n(X)=m,\ \ n(Y)=n$
• Let there be a relation R defined from X to Y.  
• A relation between two sets consists of all ordered pairs possible such that with one element is from each set.
• Then the number of such relations possible from X to Y are given by $2^{mn}$.  
• Now here we have two sets A and B such that, $A={1,2,3,4,5}\ \ \ \ ->n(A)=5$  
• Let $n(B)=b$ and number of relations are $1024=2^{10}$ hence we have,              $5b=10\\->b=2$  
• Number of elements in the set B are two.