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 $R$ 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 $A=\{1,2,3,4\}, B=\{1,5,9,11,15,16\}$ and $f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$
Are the following true?

$f$ is a relation from $A$ to $B$

Justify your answer in each case.

Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$

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

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

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

in set - bulider form,

What is its domain and range ?