00:01
In this question we need to use the mathematical induction to show that n lines in the plane passes through the same point divide the planes to 2n parts.
00:11
Okay, so we have to show this n lines in the plane passing through the same point passing through same point they divide the plane to 2n parts divide plane into 2n parts we have to prove this using induction.
00:42
So let's say for n equals to 1 one line divides the plane into 2 only one line divides the plane into 2 that is obvious.
01:02
So i would say that my p1 is true.
01:05
So for n equals to 1 we are getting the result for n equals to 2 if you see two lines passing through the same point two line passing through the same point divide the plane into 4 plane into 4 like let's say this is the point and these are the two lines this is the first line and this is the second line so we can see this is first part second part third part and fourth part so this is also true.
01:48
So what i will do i will assume that n lines it divides the plane into 2n parts.
02:00
We will prove that 2n sorry n plus 1 lines will divide the plane into 2 times n plus 1 that is 2n plus 2 parts.
02:15
So let us see how we are going to prove this.
02:25
So we can say from our assumption that since n lines passing through the same point passing through the same points they divide the plane into 2 times n parts.
02:57
Now adding one line passing through the same point now adding one line which is in the same plane and it is also passing through the same point passing through the same point it divide the corresponding two parts into four parts...