In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$ and R be a relation on A defined by $xRy$ if and only if $2x - y \in \{0, 1\}$. 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 $P(S)$ denote the power set of $S=${$1, 2, 3, …, 10$}. Define the relations $R_1$ and $R_2$ on $P(S)$ as $AR_1B$ if $(A \cap B^c) \cup (B \cap A^c) = \emptyset$ and $AR_2B$ if $A \cup B^c = B \cup A^c$, $\forall A, B \in P(S)$. Then :

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 ________.

The number of elements in the set $\{ n \in Z:|{n^2} - 10n + 19| < 6\} $ is _________.