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

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

roster form

What is its domain and range?

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

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

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

Let $A=\{1,2,3, \ldots, 14\} .$ Define a relation $R$ from $A$ to $A$ by $R = \{ (x,y):3x – y = 0,$ where $x,y \in A\} .$ Write down its domain, codomain and range.