Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $

Find the domain of $R$

Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that

$(a, a) \in R$ for all $a \in Q$

$A=\{1,2,3,5\}$ and $B=\{4,6,9\} .$ Define a relation $R$ from $A$ to $B$ by $R = \{ (x,y):$ the difference between $ x $ and $ y $ is odd; ${\rm{; }}x \in A,y \in B\} $ Write $R$ in roster form.

Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, b) \in R,$ implies $(b, a) \in R$

Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, b) \in R ,(b, c) \in R$ implies $(a, c) \in R$