Define a relation $R$ on $A=\{1, 2, 3, 4\}$ as $x R y$ if $x$ divides $y$. $R$ is

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

Let $R$ be the relation on the set $\mathbb{R}$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation on $A$,given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is:

Let $A$ be a non-empty set of children in a family. The relation $R$ is defined on $A$ as '$x$ is a brother of $y$'. This relation is:

Let $S = \{1, 2, 3, \ldots, 10\}$. Suppose $M$ is the set of all subsets of $S$. Then the relation $R = \{(A, B) : A \cap B \neq \phi; A, B \in M\}$ is :