Let $A = \{ (\alpha, \beta) \in R \times R : |\alpha - 1| \leq 4 \text{ and } |\beta - 5| \leq 6 \}$ and $B = \{ (\alpha, \beta) \in R \times R : 16(\alpha - 2)^2 + 9(\beta - 6)^2 \leq 144 \}$. Then

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

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 _____________.

Consider the following relations $R = \{(x, y) | x, y$ are real numbers and $x = wy$ for some rational number $w\}$; $S = \{(\frac{m}{n}, \frac{p}{q}) | m, n, p$ and $q$ are integers such that $n, q \neq 0$ and $qm = pn\}$. Then

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