I am self studing munkres topology book. I don't understand the example.
Definition: Suppose that A abd B are two sets with order $<_{A}$ and $<_{B}$ respectively. Define an order relation $<$ on $A×B$ by defining $a_1 ×b_1 < a_2 × b_2$ if $a_1 <_A a_2$ or if $a_1 = a_2 $ and $b_1 <_B b_2 $. It is called the dictionary order relation on $A×B$
Example 11:Consider the dictionary order on the plane $\mathbb{R} ×\mathbb{R}$. In this order the point p is less than every point lying above it on the vertical line through p, and p is less than every point to the right of this vertical line.
In $\mathbb{R} ×\mathbb{R}$ how the dictionary order relation $p<q$ imply $q$ is to the right of vertical line $p$ is on ,or above it on the same vertical line?