Hope that helps!

--Stuart Anderson

axiom 1: every line is a set of points.
axiom 2: for each line 'L' there is a point not on 'L'.
axiom 3: there exists at least 2 points.
axiom 4: for every pair of distinct points, there is one and only one line containing these points.

show that there are at least three lines.

so i m v8ing to hear from you people soon.

Good. You have to understand the problem before starting to solve it.

>axiom 1: every line is a set of points.
>axiom 2: for each line 'L' there is a point not on 'L'.
>axiom 3: there exists at least 2 points.
>axiom 4: for every pair of distinct points, there is one and
>only one line containing these points.
>
>show that there are at least three lines.

>so i m v8ing to hear from you people soon.

This is not a nice thing to say. We people have our schedules - sometimes pretty tense. Just say thank you.

Please try to think. Draw as you do and answer the three questions below:

What does #3 say?
What does #4 add to this?
What does #2 add to this?

is this ok or not.
thanks in advance.

By A3, there are two distinct points. It's up to you to pick a and b distinct. A3 only says that you can do that. So do.

>now A4 says these 2 points lies on only one line.

Essentially they lie on a line, say L. That L is unique is not important at this point.

>but by A2 there exists another line not containing point b
>and again by A2 another line not containing point a.
>So according to my consideration this geometry has at least
>three lines.

By A2, there is a point c not on L. This makes c distinct from a and b because both are on L.

By A4, there is a line La through c and a and line Lb through c and b. The three lines L, La, Lb must be distinct because otherwise the three points a, b, c would lie on a single line but, since c is not on L, the line would be different from L but still pass through a and b. This would make two lines through a and b, contradicting uniqueness in A3.

>
>is this ok or not.
>thanks in advance.