Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$. Then the number of elements in the relation $R = {((a_1, b_1), (a_2, b_2)) \in (A \times B, A \times B) : a_1$ divides $b_2$ and $a_2$ divides $b_1}$ is :

If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :

Let $A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $ and $B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } } $. Then A + B is equal to _____________.

Let $A = \{-2, -1, 0, 1, 2, 3\}$. Let R be a relation on $A$ defined by $xRy$ if and only if $y = \max\{x, 1\}$. Let $l$ be the number of elements in R. Let $m$ and $n$ be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then $l + m + n$ is equal to

The number of relations on the set $A=\{1,2,3\}$, containing at most 6 elements including $(1,2)$, which are reflexive and transitive but not symmetric, is __________.