Number of Relations for Two or More Sets

Q. The number of relations defined from the set of letters of the word 'DIGITAL' to the set of letters of the word 'OFFLINE' is

1. $7^7$
2. $2^{6^2}$
3. $2^{7^2}$
4. $6^6$

Q. If the total number of relations from a set A to a set B is $2,$ then find the type of sets A and B.

1. $A$ is a empty set and $B$ is a singleton set
2. $B$ is a empty set and $A$ is a singleton set
3. None of the above
4. Both $A$ and $B$ is singleton sets

Q. Number of possible relations from the set A to set B, where $n\left(A\right)=2,n\left(B\right)=5$ is

Q. If a set $A$ has ${}^{\prime }{n}^{\prime }$ distinct elements, then the number of all relations on $A$ is

1. $2^{n^n}$
2. $2^{n^2}$
3. $2^n$
4. $n^2$

Q. Let \(n (A) = m\) and \(n (B) = n.\) Then, the total number of non-empty relations that can be defined from \(A\) to \(B\) is .