Let $A = {0, 1, 2, 3, 4, 5}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max{x, y} \in {3, 4}$. Then among the statements (S1): The number of elements in $R$ is $18$, and (S2): The relation $R$ is symmetric but neither reflexive nor transitive

Let the relations $R_1$ and $R_2$ on the set $X = \{1, 2, 3, ..., 20\}$ be given by $R_1 = \{(x, y) : 2x - 3y = 2\}$ and $R_2 = \{(x, y) : -5x + 4y = 0\}$. If $M$ and $N$ be the minimum number of elements required to be added in $R_1$ and $R_2$, respectively, in order to make the relations symmetric, then $M + N$ equals

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.

If A = {x $\in$ R : |x $-$ 2| > 1}, B = {x $\in$ R : $\sqrt {{x^2} - 3} $ > 1}, C = {x $\in$ R : |x $-$ 4| $\ge$ 2} and Z is the set of all integers, then the number of subsets of the set (A $\cap$ B $\cap$ C)c $\cap$ Z is ________________.

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 _____________.