 Let us see how we can represent line segment array and a line in set notations. So let us first take an example of a line segment. Here you see the line segment AB, so let me just write it as segment AB with its notation. I can describe the line segment AB as points A and B and every point that lies between A and B. Now this description is going to help us write the set notation. Let us focus on the first part point A and B. So let us try and write segment AB in the set notation. So the first part, let me write it in orange. So it's the point A and B which we can write by using curly brackets and writing A, B. That means we are just considering point A and B union, union means and and now we will write the notation for this statement every point that lies between A and B. So now let us consider there is some point P. I will just draw some point P. Now P can be anywhere between A and B. So point P is such that point P is between A and B. So the notation that you see here A dash P dash B means that point P is between A and B. And when we say point P is between A and B, all three points are collinear. Remember that. So now this completes the description of line segment AB. Let us try and rewrite the line segment AB set notation. So it is point A and B union every point P such that P is between points A and B. And if we were to draw this diagram, this is how it will look like. Points A and B and some point P between them. Now let us see how we can represent ray. So we want to represent a ray and let's say this ray is ray AB. Now this ray AB would look like this. Since we are reading it as ray AB, so A is a terminal point and the ray extends after B. So let us assume there is some point C after B such that now B is between A and C. How can we write this ray AB in set notation now? We can write ray AB such that it's the union of the segment AB. So segment AB which is this part and all the points that extend after B and these all points can be described by some point C such that point B is between points A and C. That just means that C could be anywhere after B with the required condition that B is between A and C. So let us rewrite the notation for ray AB. So ray AB would be line segment AB union every point C such that point B is between points A and C and this is how it will look like. Now what about ray BA? Now B will be the terminal point. This ray BA would look something like this. So ray, so this is point B and this is point A, so the terminal point is B and the other point is A. Now we will have some point C after A to the left and A is between B and C now. So this set notation would be segment AB union some point C such that point A is between C and B. Now we want to see the set notation for a line. So let's draw a line. So this is how we can draw a line. Let's say this is point A and this is point B and we want to plot one more point say O between A and B. We can write the set notation for line AB by different many ways. One of the ways is writing the union of ray OA and ray OB. But union of ray OA and OB could be like this as well but this is not a line. We need to ensure that A OB are collinear and one way to write that is to make sure that we mention that point O is between A and B. So the description for the line would be line AB is equal to ray OA union ray OB such that point O is between points A and B. Another way is to write union of ray BA. So this part and ray AB. So we can write line AB to be the union of ray BA and ray AB. That just ensures that the set of points extend before A as well as after B. So let's just summarize few important ways. So let us draw a line AB here like this and let's put point O in between. So line AB can be described by a set notation as the union of ray OA and ray OB provided point O is between A and B. Another way would be to write the union of ray BA which is this and then ray AB which goes towards right. Another way I can think of writing line AB in set notation is by considering two more points C and D like that and we can we can write it is the union of segment AB and some point C such that B is between A and C and some point D such that A is between D and B and these are many ways in which we can write line AB in a set notation.