The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by

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 $(a, c) \in R$

Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.

$A=\{1,2,3,5\}$ 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.

The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation

roster form

What is its domain and range?