I'm having trouble understanding what this problem is asking me

Question

This is the problem

So my problem is that I dont know how to solve it... I have learned about system of inequalities and that kinda stuff, but I never got anything like this. I do not want anyone to solve the problem for me, however If you could explain to me what the problem is asking me to do in a less complicated form that would help, also after you explain, could you tell me how it relates to lines, points, regions, and no intersection. If its impossible to explain this to me without solving then I'm fine with that, but if its possible not to that'd be great Thank you for the help

P.S: I understand what lines and regions are but im also a little confused with what they mean by a point, and no intersection.

Answer 1

A set theoretic explanation:

An object (line or a graph) is basically a set of points in $\Bbb{R}^2$.

Let there be 2 objects $O_1$ and $O_2$.

The question asks..

Does there exist $O_1\ \&\ O_2$ such that

a. $O_1\cap O_2=\{\text{exactly $1$ point}\}$

b. $O_1\cap O_2=\{y:\text{If } y_1,y_2,y_3\in O_1\cap O_2, y_1,y_2,y_3 \text{ form a straight line }\}$

c. $O_1\cap O_2=\{x:\text{the area of the region containing the $x$'s is $\gt 0$}\}$

d. $O_1\cap O_2=\{\phi\}$