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 range of $R$

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?

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

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 $a \in Q$

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?

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

Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$