What do you mean by a binary relation on a set $A$?

Define the domain and range of a binary relation on $A$.

Let $A=\{2, 3, 5\}$ and $R=\left\{\right(2, 3), (2, 5), (3, 3), (3, 5\left)\right\}$

Show that $R$ is a binary relation on $A$.

Let $A=\{2, 3, 5\}$ and $R=\left\{\right(2, 3), (2, 5), (3, 3), (3, 5\left)\right\}$

Find domain and range of $R$.

Let $A=\{0, 1, 2, 3, 4, 5, 6, 7, 8\}$ and let $R=\left\{\right(a, b): a, b\in A$ and $2a+3b=12\}$.

Express $R$ as a set of ordered pairs. Show that $R$ is a binary relation on $A$.

Let $A=\{0, 1, 2, 3, 4, 5, 6, 7, 8\}$ and let $R=\left\{\right(a, b): a, b\in A$ and $2a+3b=12\}$.

Find its domain and range.

If $R$ is a binary relation on a set $A$, define $R^{-1}$ on $A$.

Let $R=\left\{\right(a, b):a, b\in W$ and $3a+2b=15\}$, where $W$ is the set of whole numbers.

Express $R$ and $R^{-1}$ as sets of ordered pairs.

Let $R=\left\{\right(a, b):a, b\in W$ and $3a+2b=15\}$, where $W$ is the set of whole numbers.

Show that Domain$\left(R\right)=$range$\left(R^{-1}\right)$

What is an equivalence relation?

Let $R=\left\{\right(a, b): a, b\in Z$ and $(a-b)$ is even$\}$.

Then, show that $R$ is an equivalence relation on $Z$.