The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?
It is obvious that the relation $R$ is $" x$ is the square of $y''$
In roster form, $R=\{(9,3),(9,-3),(4,2),(4,-2),(25,5),(25,-5)\}$
The domain of this relation is $\{4,9,25\} .$
The range of this relation is $\{-2,2,-3,3,-5,5\}$
Note that the element $1$ is not related to any element in set $P$.
The set $Q$ is the codomain of this relation.
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Depict this relation using an arrow diagram.
Write the relation $R = \{ \left( {x,{x^3}} \right):x$ is a prime number less than $10{\rm{\} }}$ in roster form.
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 $(a, c) \in R$
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?
$(a, a) \in R ,$ for all $a \in N$
Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$