Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Find the number of relations from $A$ to $B$.

Let $A = \{1, 2, 3, \ldots, 10\}$ and $R$ be a relation on $A$ such that $R = \{(a, b) : a = 2b + 1\}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$,for which such a sequence exists,is equal to:

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is:

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Depict this relation using an arrow diagram.

Let $A$ be the set of even natural numbers that are $< 8$ and $B$ be the set of prime integers that are $< 7$. The number of relations from $A$ to $B$ is: