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:

Consider the relations $R_1$ and $R_2$ defined as $aR_1b \Leftrightarrow a^2 + b^2 = 1$ for all $a, b \in R$ and $(a, b)R_2(c, d) \Leftrightarrow a+ d = b + c$ for all $(a, b), (c, d) \in N \times N$. Then:

Let R be a relation defined on $N$ as $aRb$ if $2a + 3b$ is a multiple of $5$, $a, b \in N$. Then R is

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 $A = {n \in [100, 700] \cap N : n$ is neither a multiple of 3 nor a multiple of 4}. Then the number of elements in $A$ is